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Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?
Answer & Solution
Correct Answer:
Option
B
$$\eqalign{
& {\text{Draw}} \bot OY{\text{ on }}AC \cr
& {\text{So, }}AY = YC \cr} $$
$$\eqalign{ & AX = BX\,\,\left[ {\because OX \bot AB} \right] \cr & \because \Delta AYX \cong \Delta ABC \cr & \frac{{AY}}{{AC}} = \frac{{XY}}{{BC}} \cr & \frac{{AY}}{{2AY}} = \frac{{XY}}{{BC}} \cr & XY = \frac{1}{2}BC \cr} $$
$$\eqalign{ & AX = BX\,\,\left[ {\because OX \bot AB} \right] \cr & \because \Delta AYX \cong \Delta ABC \cr & \frac{{AY}}{{AC}} = \frac{{XY}}{{BC}} \cr & \frac{{AY}}{{2AY}} = \frac{{XY}}{{BC}} \cr & XY = \frac{1}{2}BC \cr} $$
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