Question

in the given figure, AB and CD are two equal chords of a circle, with the center O.
IF P is the mid-point of chord AB .Q is the mid- point of chord CD and $\angle POQ={150}^{\circ },findthe\angle APQ.$

Answer 1

Since $AB=CD$ (equal chords) so, their distance from centre must le equal

So, $OP=OQ$

Now, In $△POQ$

(1) $\angle OPQ=\angle OQP$

(2) $\angle OPQ+\angle OQP+\angle POQ={180}^0$

$\Rightarrow 2\angle OPQ+{150}^0={180}^0$

$\Rightarrow \angle OPQ={15}^0$

Also, $\because P$ is midpoint of $AB$

$OP\perp AB\Rightarrow \angle APO={90}^0$

Now, $\angle APQ=\angle APO-\angle OPQ={90}^0-{15}^0={75}^0$