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 $\angle POQ={100}^{\circ }$, the measure of $\angle APQ$ is:

• A. ${45}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is B

${50}^{\circ }$

AB = CD, hence OP = OQ, given $\angle POQ={100}^{\circ }$

Then $\angle OPQ={40}^{\circ }$

$\angle APQ={130}^{\circ }$

If we interchange positions of A & B,

$\angle APQ={50}^{\circ }$.