Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?
A. BC
B. $$\frac{1}{2}$$ BC
C. $$\frac{1}{3}$$ BC
D. $$\frac{1}{4}$$ BC
Answer: Option B
Solution (By Examveda Team)
$$\eqalign{ & {\text{Draw}} \bot OY{\text{ on }}AC \cr & {\text{So, }}AY = YC \cr} $$
$$\eqalign{ & AX = BX\,\,\left[ {\because OX \bot AB} \right] \cr & \because \Delta AYX \cong \Delta ABC \cr & \frac{{AY}}{{AC}} = \frac{{XY}}{{BC}} \cr & \frac{{AY}}{{2AY}} = \frac{{XY}}{{BC}} \cr & XY = \frac{1}{2}BC \cr} $$
This Question Belongs to Arithmetic Ability >> Geometry
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