Question

$AB$ and $CD$ are two equal chords of a circle with centre at $O.$ If $OP\perp AB$ and $OQ\perp CD,$ where $P$ and $Q$ are points on the chords $AB$ and $CD$ respectively and if $\angle POQ=100°,$ the measure of $\angle APQ$ is :

• A. ${135}^{\circ }$
• B. ${130}^{\circ }$
• C. ${120}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is B ${130}^{\circ }$


$AB=CD,$ hence $OP=OQ,$
Given $\angle POQ={100}^{\circ }$
then $\angle OPQ={40}^{\circ }$
$\angle BPQ={50}^{\circ }\Rightarrow \angle APQ={130}^{\circ }$