Two circles with centres at $A$ and $B$, touch at $T.BD$ is the tangent at $D$ and $TC$ is a common

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Two circles with centres 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:

Accepted Answer

Sol. [Key Concept: Apply the same chord/tangent relation as the stem to evaluate this option set.]$$\begin{matrix} & BC = \frac{2}{cos	heta} = \frac{2}{\frac{4}{5}} = \frac{5}{2} \ & CD = 4 - \frac{5}{2} = \frac{3}{2} \end{matrix}$$

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