Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Draw}\perp OY\text{ on }AC\\ & \text{So, }AY=YC\end{array}$$

$$\begin{array}{rl}& AX=BX\left[\because OX\perp AB\right]\\ & \because \Delta AYX\cong \Delta ABC\\ & \frac{AY}{AC}=\frac{XY}{BC}\\ & \frac{AY}{2AY}=\frac{XY}{BC}\\ & XY=\frac{1}{2}BC\end{array}$$