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Offline Centres

Q.

Two circles with centers at A and B, touch at T. BD is the tangent at D and TC is a common tangent. AT has length 3 and BT has length 2. The length of CD is

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a

7/4

b

3/2

c

5/3

d

4/3

answer is B.

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Detailed Solution

$\begin{array}{l} G i v e n t h a t \\ A T = 3, B T = 2 \Rightarrow A B = 5 \\ A D = 3, A D ⊥ B D \\ ∆ A B D i s r i g h t a n g l e d a t D \Rightarrow B D = 4 \\ a n d CD = CT (l e n g t h o f \tan g e n t) \\ ∆ B T C a n d ∆ A D B a r e similar \\ \Rightarrow \frac{BT}{BD} = \frac{CT}{AD}, \frac{2}{4} = \frac{CT}{3} \Rightarrow CT = \frac{3}{2} \end{array}$

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