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CAT 1996 | Question: 115

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By Appollonius theorem,  

(AB)2 + (BC)2 = 2((AD)2 + (BD)2)

AD = 3 since D is the midpoint of AC

(AC)2 = 2(32 + (BD)2)   ....{ (AB)2 + (BC)2 = (AC)2 using Pythagoras theorem }

$\therefore$ 62 = 2(9 + (BD)2)

On solving, we get BD = 3.

 

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