Question

Two concentric circles, shown in the given figure, have a common centre O.A line l int the outer circle at A and B and the inner circle at C and D. If AB =x and CD =y, Prove AC =BD =$\frac{1}{2}(x-y)$

Answer 1

Drop a perpendicular from O to given chord.
Now, we know that, parpemdicular form the centre to the chord bisects
the chord.
$\therefore PD=\frac{y}{2}andPB=\frac{x}{2}\therefore BD=PB-PD=\frac{x}{2}-\frac{y}{2}=\frac{1}{2}(x-y)AC=\frac{1}{2}(x-y)$