Question

In the given figure, $APB$ is tangent at $P$ to the circle with the centre $O$. If $\angle QPB={60}^o$ then measure of $\angle POQ=$

• A. ${60}^o$
• B. ${30}^o$
• C. ${120}^o$
• D. ${90}^o$

Answer 1

Answer: (C)

${120}^o$

Given that:

$\angle QPB={60}^{\circ }$

To find:

$\angle POQ=?$

Solution:

$\angle QPB=\angle QRP={60}^{\circ }$ (Alternate segment theorem)

$\angle POQ=2\angle QRP=2\times {60}^{\circ }={120}^{\circ }$ (Angle subtended by the chord at the centre is twice of angle subtended by it at circumference.)

Hence, C is the correct option.