Question

Given : A circle with centre O and P is the mid-point of its chord AB.
then, OP is perpendicular to AB.
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

In $△$s OPA and OPB,
OP = OP (Common)
OA = OB (Radius of the circle)
AP = BP (P is the mid point of AB)
Hence, $△OPA\cong △OPB$ (SSS rule)
Thus, $\angle OPA=\angle OPB=x$ (By cpct)
$\angle OPA+\angle OPB=180$ (Angles on a straight line)
$x+x=180$
$x=90$
$\angle OPA=\angle OPB={90}^{\circ }$
or, OP is perpendicular to AB