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

Solution (By Examveda Team)

$$\eqalign{ & {\text{Draw}} \bot OY{\text{ on }}AC \cr & {\text{So, }}AY = YC \cr} $$

$$\eqalign{ & AX = BX\,\,\left[ {\because OX \bot AB} \right] \cr & \because \Delta AYX \cong \Delta ABC \cr & \frac{{AY}}{{AC}} = \frac{{XY}}{{BC}} \cr & \frac{{AY}}{{2AY}} = \frac{{XY}}{{BC}} \cr & XY = \frac{1}{2}BC \cr} $$