Question

The line drawn through the center of a circle to bisect a chord is perpendicular to the chord. Prove this statement.

Answer 1

Here $AP=PB$

$OA=OB$ (radius)

$OP=OP$ (common)

$\Rightarrow △POA\cong △POB$

$\Rightarrow \angle APO=\angle BPO$,

But $\angle APO+\angle BPO={180}^{\circ }$ [$\because$ linear pair]

$\Rightarrow 2\angle APO={90}^{\circ }$

$\Rightarrow \angle APO=\angle BPO={90}^{\circ }$