Recent questions tagged geometry / Aptitude Overflow

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161

CAT 2003 | Question: 1-130
There are two concentric circles such that the area of the outer circle is four times of the area of inner circle. Let A, B and C be the three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is ... $\pi \sqrt{12}$ $\frac{9}{\pi}$ $\frac{9 \sqrt{3} }{\pi}$ $\frac{6 \sqrt{3} }{\pi}$

There are two concentric circles such that the area of the outer circle is four times of the area of inner circle. Let A, B and C be the three distinct points on the peri...

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go_editor asked Feb 8, 2016

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162

CAT 2003 | Question: 1-127
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is $90^{\circ}$ or concanve if the internal angle is $270^{\circ}$. If the number of convex corners in such a polygon is $25,$ the number of concave corners must be $20$ $0$ $21$ $22$

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is $90^{\circ}$ or concanve ...

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13.8k points

430 views

go_editor asked Feb 8, 2016

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163

CAT 2014 | Question: 49
Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}$. The circles have the same radii and neither $\text{P}$ nor $\text{Q}$ falls within the intersection of the circles. What is the smallest range that ... $\text{AQP}$ in degrees? Between $0$ and $90$ Between $0$ and $30$ Between $0$ and $60$ Between $0$ and $75$

Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}$. The circles have the same radii and neither $\text{P}$...

makhdoom ghaya

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makhdoom ghaya asked Jan 17, 2016

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164

CAT 2014 | Question: 27
The line $\text{AB}$ is $6$ metres in length and is tangent to the inner one of the two concentric circles at point $\text{C}.$ It is known that the radii of the two circles are integers. The radius of the outer circle is $5$ metres $4$ metres $6$ metres $3$ metres

The line $\text{AB}$ is $6$ metres in length and is tangent to the inner one of the two concentric circles at point $\text{C}.$ It is known that the radii of the two circ...

makhdoom ghaya

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811 views

makhdoom ghaya asked Jan 16, 2016

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1 answer

165

CAT 2014 | Question: 10
A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle? $2 : 3$ $3 : 4$ $1 : 4$ $1 : 2$

A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circums...

makhdoom ghaya

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makhdoom ghaya asked Jan 16, 2016

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166

CAT 2004 | Question: 73
A circle with radius $2$ is placed against a right angle. Another small circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle? $3-2 \sqrt{2}$ $4-2 \sqrt{2}$ $7-4 \sqrt{2}$ $6-4 \sqrt{2}$

A circle with radius $2$ is placed against a right angle. Another small circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?$...

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go_editor asked Jan 14, 2016

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167

CAT 2004 | Question: 69
Let $\text{C}$ be a circle with centre $\text{P}_0$ and $\text{AB}$ be a diameter of $\text{C}.$ suppose $\text{P}_1$ is the mid-point of the line segment $\text{P}_0\text{B}, \text{P}_2$ is the mid-point of the line segment $\text{P}_1\text{B}$ and ... the area of the unshaded portion of $\text{C}$ to that of the original circle $\text{C}$ is $8:9$ $9:10$ $10:11$ $11:12$

Let $\text{C}$ be a circle with centre $\text{P}_0$ and $\text{AB}$ be a diameter of $\text{C}.$ suppose $\text{P}_1$ is the mid-point of the line segment $\text{P}_0\tex...

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go_editor asked Jan 14, 2016

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168

CAT 2014 | Question: 3
From a circular sheet of paper with a radius $20$ cm, four circles of radius $5$ cm each are cut out. What is the ratio of the uncut to the cut portion? $1:3$ $4:1$ $3:1$ $4:3$

From a circular sheet of paper with a radius $20$ cm, four circles of radius $5$ cm each are cut out. What is the ratio of the uncut to the cut portion? $1:3$$4:1$$3:1$$4...

makhdoom ghaya

8.1k points

414 views

makhdoom ghaya asked Jan 13, 2016

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169

CAT 2014 | Question: 1
If $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle, what is the measure of angle $\angle \text{DEC}?$ $15^{\circ}$ $30^{\circ}$ $20^{\circ}$ $45^{\circ}$

If $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle, what is the measure of angle $\angle \text{DEC}?$ $15^{\circ}$$30^{\circ}$$20^{\circ}$$45^{\circ...

makhdoom ghaya

8.1k points

483 views

makhdoom ghaya asked Jan 13, 2016

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170

CAT 2004 | Question: 60
On a semicircle with diameter AD; chord BC is parallel to the diameter. Further, each of the chords AB and CD has length $2,$ while has length $8.$ What is the length of BC? $7.5$ $7$ $7.75$ None of the above

On a semicircle with diameter AD; chord BC is parallel to the diameter. Further, each of the chords AB and CD has length $2,$ while has length $8.$ What is the length of ...

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13.8k points

634 views

go_editor asked Jan 13, 2016

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171

CAT 2004 | Question: 59
In the adjoining figure, chord $\text{ED}$ is parallel to the diameter $\text{AC}$ of the circle. If $\angle \text{CBE} = 65^{\circ}$ then what is the value of $\angle \text{DEC}?$ $35^{\circ}$ $55^{\circ}$ $45^{\circ}$ $25^{\circ}$

In the adjoining figure, chord $\text{ED}$ is parallel to the diameter $\text{AC}$ of the circle. If $\angle \text{CBE} = 65^{\circ}$ then what is the value of $\angle \t...

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go_editor asked Jan 13, 2016

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172

CAT 2004 | Question: 56
Answer the question on the basis of the information given below: In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line ... cm. What is the ration of the length of PQ to that of QO? $1:4$ $1:3$ $3:8$ $3:4$

Answer the question on the basis of the information given below:In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch eac...

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13.8k points

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go_editor asked Jan 13, 2016

1 votes

1 answer

173

CAT 2004 | Question: 55
A rectangular sheet of paper, when halved by folding it at mid-point of its longer side, results in a rectangle, whose longer and shorter sides are in same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is ... is the area of the smaller rectangle? $4 \sqrt{2}$ $2 \sqrt{2}$ $ \sqrt{2}$ None of the above

A rectangular sheet of paper, when halved by folding it at mid-point of its longer side, results in a rectangle, whose longer and shorter sides are in same proportion as ...

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go_editor asked Jan 12, 2016

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174

CAT 2009 | Question: 19
There are three coplanar parallel lines. If any $p$ points are taken on each of the lines, then find the maximum number of triangles with the vertices of these points. $p^{2}(4p-3)$ $p^{3}(4p-3)$ $p(4p-3)$ $p^{3}$

There are three coplanar parallel lines. If any $p$ points are taken on each of the lines, then find the maximum number of triangles with the vertices of these points.$p^...

makhdoom ghaya

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makhdoom ghaya asked Dec 31, 2015

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175

CAT 2009 | Question: 18
M is the center of the circle. $l(\text{QS})=10 \sqrt{2},l (\text{PR}) = l(\text{RS})$ and $\text{PR} \| \text{QS}$. Find the area of the shaded region. (use $\pi=3$) $100$ sq. units $114$ sq. units $50$ sq. units $200$ sq. units

M is the center of the circle. $l(\text{QS})=10 \sqrt{2},l (\text{PR}) = l(\text{RS})$ and $\text{PR} \| \text{QS}$. Find the area of the shaded region. (use $\pi=3$)$100...

makhdoom ghaya

8.1k points

543 views

makhdoom ghaya asked Dec 31, 2015

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1 answer

176

CAT 2005 | Question: 30
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is $10$ $12$ $14$ $16$

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tile...

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13.8k points

872 views

go_editor asked Dec 29, 2015

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177

CAT 2005 | Question: 24
$\text{P, Q, S}$ and $\text{R}$ are points on the circumference of a circle of radius $r,$ such that $\text{PQR}$ is an equilateral triangle and $\text{PS}$ is a diameter of the circle. What is the perimeter of the quadrilateral $\text{PQSR}?$ $2r(1+\sqrt{3})$ $2r(2+\sqrt{3})$ $r(1+\sqrt{5})$ $2r +\sqrt{3}$

$\text{P, Q, S}$ and $\text{R}$ are points on the circumference of a circle of radius $r,$ such that $\text{PQR}$ is an equilateral triangle and $\text{PS}$ is a diameter...

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13.8k points

401 views

go_editor asked Dec 29, 2015

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178

CAT 2005 | Question: 23
Consider the triangle $\text{ABC}$ shown in the following figure where $\text{BC = 12 cm, DB =9 cm, CD=6 cm,}$ and $\angle \text{BCD} = \angle \text{BAC}.$ What is the ratio of the perimeter of the triangle $\text{ADC}$ to that of the triangle $\text{BDC}?$ $7/9$ $8/9$ $6/9$ $5/9$

Consider the triangle $\text{ABC}$ shown in the following figure where $\text{BC = 12 cm, DB =9 cm, CD=6 cm,}$ and $\angle \text{BCD} = \angle \text{BAC}.$ What is the ra...

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13.8k points

455 views

go_editor asked Dec 29, 2015

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179

CAT 2005 | Question: 22
In the following figure, the diameter of the circle is $3$ cm. $\text{AB}$ and $\text{MN}$ are two diameters such that $\text{MN}$ is perpendicular to $\text{AB.}$ In addition, $\text{CG}$ is perpendicular to $\text{AB}$ such that $\text{AE : EB} = 1 : 2,$ and $\text{DF}$ is ... cm is $2\sqrt{2} -1$ $((2\sqrt{2} -1 ))/2$ $((3\sqrt{2} -1 ))/2$ $((2\sqrt{2} -1 ))/3$

In the following figure, the diameter of the circle is $3$ cm. $\text{AB}$ and $\text{MN}$ are two diameters such that $\text{MN}$ is perpendicular to $\text{AB.}$ In add...

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13.8k points

585 views

go_editor asked Dec 29, 2015

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180

CAT 2005 | Question: 20
Rectangular tiles each of size $70$ cm by $30$ cm must be laid horizontally on a rectangular floor of size $110$ cm by $130$ cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges on ... overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is $4$ $5$ $6$ $7$

Rectangular tiles each of size $70$ cm by $30$ cm must be laid horizontally on a rectangular floor of size $110$ cm by $130$ cm, such that the tiles do not overlap. A til...

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13.8k points

534 views

go_editor asked Dec 29, 2015

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181

CAT 2005 | Question: 17
Four points $\text{A, B, C}$ and $\text{D}$ lie on the straight line in $\text{X-Y}$ plane, such that $\text{AB = BC = CD}$ and the length of $\text{AB}$ is $1$ meter. An ant at $\text{A}$ wants to reach a sugar particle at $\text{D}.$ ... . The minimum distance in meters the ant must traverse to reach the sugar particle is $3\sqrt{2}$ $1 + \pi$ $\frac{4 \pi}{3}$ $5$

Four points $\text{A, B, C}$ and $\text{D}$ lie on the straight line in $\text{X-Y}$ plane, such that $\text{AB = BC = CD}$ and the length of $\text{AB}$ is $1$ meter. An...

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13.8k points

461 views

go_editor asked Dec 29, 2015

1 votes

1 answer

182

CAT 2005 | Question: 12
Consider a triangle drawn on the $\text{X-Y}$ plane with its three vertices at $(41, 0), (0, 41),$ and $(0, 0)$ each vertex being represented by its $\text{(X, Y)}$ coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is $780$ $800$ $820$ $741$

Consider a triangle drawn on the $\text{X-Y}$ plane with its three vertices at $(41, 0), (0, 41),$ and $(0, 0)$ each vertex being represented by its $\text{(X, Y)}$ coord...

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go_editor asked Dec 29, 2015

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183

CAT 2005 | Question: 09
What is the distance in cm between two parallel chords of length $32$ cm and $24$ cm in a circle of radius $20$ cm? $1$ or $7$ $2$ or $14$ $3$ or $21$ $4$ or $28$

What is the distance in cm between two parallel chords of length $32$ cm and $24$ cm in a circle of radius $20$ cm?$1$ or $7$$2$ or $14$$3$ or $21$$4$ or $28$

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13.8k points

692 views

go_editor asked Dec 29, 2015

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184

CAT 2005 | Question: 03
Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side $1$ cm. The area in sq. cm of the portion that is common to the two circles is $\pi / 4$ $\frac{\pi}{2} – 1$ $\frac{\pi}{5}$ $\sqrt{2} – 1$

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side $1$ cm. The area in sq. cm of the portion that is com...

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13.8k points

809 views

go_editor asked Dec 29, 2015

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185

CAT 2006 | Question: 75
An equilateral triangle $\text{BP}$ is drawn inside a square $\text{ABCD}.$ What is the value of the angle $\text{APD}$ in degrees? $75$ $90$ $120$ $135$ $150$

An equilateral triangle $\text{BP}$ is drawn inside a square $\text{ABCD}.$ What is the value of the angle $\text{APD}$ in degrees?$75$$90$$120$$135$$150$

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13.8k points

417 views

go_editor asked Dec 28, 2015

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1 answer

186

CAT 2006 | Question: 71
A semi-circle is drawn with $\text{AB}$ as its diameter. From $\text{C}$, a point on $\text{AB,}$ a line perpendicular to $\text{AB}$ is drawn meeting the circumference of the semi-circle at $\text{D.}$ Given that $\text{AC = 2 cm}$ and $\text{CD = 6 cm}$ the area of the semi-circle (in sq. cm) will be $32 \pi$ $50 \pi$ $40.5 \pi$ $81 \pi$ undeterminable

A semi-circle is drawn with $\text{AB}$ as its diameter. From $\text{C}$, a point on $\text{AB,}$ a line perpendicular to $\text{AB}$ is drawn meeting the circumference o...

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13.8k points

604 views

go_editor asked Dec 28, 2015

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187

CAT 2006 | Question: 63
Below question is on the basis of information given below: A punching machine is used to punch a circular hole of diameter $2$ units from a square sheet of aluminium of width $2$ units, as shown below. The hole is punched such that circular hole touches one corner P of the square sheet and the diameter of ... $(6- \pi) /8$ $(4- \pi) /4$ $(\pi - 2) /4$ $(14-3 \pi) /6$

Below question is on the basis of information given below:A punching machine is used to punch a circular hole of diameter $2$ units from a square sheet of aluminium of wi...

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13.8k points

411 views

go_editor asked Dec 28, 2015

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188

CAT 2007 | Question: 03
Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}.$ The circles have the same radii and neither $\text{P}$ nor $\text{Q}$ falls within the intersection of the circles. What is the smallest range that ... Between $0$ and $90$ Between $0$ and $30$ Between $0$ and $60$ Between $0$ and $75$ Between $0$ and $45$

Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}.$ The circles have the same radii and neither $\text{P}$...

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13.8k points

385 views

go_editor asked Dec 6, 2015

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189

CAT 2008 | Question: 23
Two circles, both of radii $1$ cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region? $\frac{\pi}{3} - \frac{\sqrt{3}} {4} $ $\frac{2 \pi}{3} + \frac{\sqrt{3}} {2} $ ... $\frac{4 \pi}{3} + \frac{\sqrt{3}} {2} $ $\frac{2 \pi}{3} - \frac{\sqrt{3}} {2} $

Two circles, both of radii $1$ cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecti...

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13.8k points

433 views

go_editor asked Nov 29, 2015

1 votes

1 answer

190

CAT 2008 | Question: 19
Consider obtuse-angled triangles with sides $8$ cm, $15$ cm and $x$ cm. If x is an integer, then how many such triangles exist? $5$ $21$ $10$ $15$ $14$

Consider obtuse-angled triangles with sides $8$ cm, $15$ cm and $x$ cm. If x is an integer, then how many such triangles exist?$5$$21$$10$$15$$14$

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13.8k points

974 views

go_editor asked Nov 28, 2015

1 votes

1 answer

191

CAT 2008 | Question: 18
Consider a square $\text{ABCD}$ with midpoints $\text{E, F, G, H}$ of $\text{AB, BC, CD}$ and $\text{DA}$ respectively. Let $\text{L}$ denote the line passing through $\text{F}$ and $\text{H}.$ Consider points $\text{P}$ and $\text{Q},$ on $\text{L}$ and inside $\text{ABCD},$ ... $2 + \sqrt{3}$ $\frac{10-3 \sqrt{3} } {9} $ $1+ \frac{1}{\sqrt{3} }$ $2 \sqrt{3} -1$

Consider a square $\text{ABCD}$ with midpoints $\text{E, F, G, H}$ of $\text{AB, BC, CD}$ and $\text{DA}$ respectively. Let $\text{L}$ denote the line passing through $\t...

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13.8k points

3.1k views

go_editor asked Nov 28, 2015

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192

CAT 2008 | Question: 07
In a triangle $\text{ABC}$, the lengths of the sides $\text{AB}$ and $\text{AC}$ equal $17.5$ cm and $9$ cm respectively. Let $\text{D}$ be a point on the line segment $\text{BC}$ such that $\text{AD}$ is perpendicular to $\text{BC}.$ ... what is the radius (in cm) of the circle circumscribing the triangle $\text{ABC}?$ $17.05$ $27.85$ $22.45$ $32.25$ $26.25$

In a triangle $\text{ABC}$, the lengths of the sides $\text{AB}$ and $\text{AC}$ equal $17.5$ cm and $9$ cm respectively. Let $\text{D}$ be a point on the line segment $\...

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13.8k points

475 views

go_editor asked Nov 28, 2015

2 votes

2 answers

193

In the given figure, ∠BAC = 120° and AD is the bisector of ∠BAC.

In the given figure, $∠BAC = 120º$ and $AD$ is the bisector of $∠BAC$. If $\frac{(AD)(AB)}{BD} = \frac{AE}{EC}( AE + EC )$ and $∠EDC = ∠ECD$, what is the ratio ...

makhdoom ghaya

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1.6k views

makhdoom ghaya asked Aug 25, 2015

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views	views:100
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answers	answers:2
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