Question

The given figure shows a circle with centre O. P is mid-point of chord AB. Then OP is parallel to AB.

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is B False

In $△$s $OAP$ and $OBP,$
$OP=OP$ (Common)
$OA=OB$ (Radius of circle)
$PA=PB$ (Given)
Thus, $△OPA\cong △OPB$ (SAS rule)
Hence, $\angle OPA=\angle OPB=x$ (By cpct)
Sum of angles, $\angle OPA+\angle OPB={180}^o$ (Angles on a straight line)
$x+x={180}^o$
$x={90}^{\circ }$
Thus, $\angle OPA=\angle OPB={90}^{\circ }$
$OP$ is perpendicular to $AB$.