# CAT2014-27

304 views

The line AB is $6$ metres in length and is tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is

1. $5$ metres
2. $4$ metres
3. $6$ metres
4. $3$ metres

Important steps to solve this question:

1. The perpendicular from center (O) to C will divide the chord AB into equal halves. Hence BC = AC = 3 metres.
2. Now, in △ OCB, ∠ OCB = 90°. Hence the sides of this triangle will obey the Pythagorean rule. Hence, OB² = OC² + BC²
3. If BC is 3 metres, the only possible Pythagorean triplet would be 3, 4 and 5. Hence OB = 5 metres.
18 points 1 1 1

## Related questions

1
212 views
Recently, Rajesh visited the local casino where he came across a new card game. Two players, using a normal deck of $52$ playing cards, play this game. One player is called the 'dealer and the other is called the 'player . First, the player picks a card at random from the ... Rajesh stopped playing the game when his loss would be maximumm, the loss in Rs. Would have been $-12$ $-20$ $-8$ $-4$
1 vote
2
426 views
Answer the questions based on following data. A dealer deals only in colour TVs and VCRs. He wants to spend up to $Rs.12$ lakhs to buy $100$ pieces. He can purchase a colour TV at $Rs.10,000$ and a VCR at $Rs.15,000$. He can sell a colour TV at $Rs.12,000$ ... from his original stock if he can sell a colour TV at $Rs.12200$ and VCR at $Rs.18300$ is $2.64$ $2.49$ $2.72$ $2.87$
1 vote
Answer the questions based on following data. A dealer deals only in colour TVs and VCRs. He wants to spend up to $Rs.12$ lakhs to buy $100$ pieces. He can purchase a colour TV at $Rs.10,000$ and a VCR at $Rs.15,000$. He can sell a colour TV at $Rs.12,000$ and a ... then for maximizing profit, the ratio of number of VCRs and number of TVs that he should stock is $7 : 3$ $0$ $1 : 2$ None of these