Question

In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle.
If $\angle$PAQ = ${50}^{\circ }$ then, find $\angle$OPQ.

• A. ${100}^{\circ }$
• B. ${12.5}^{\circ }$
• C. ${50}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is D ${25}^{\circ }$

By theorem : If two tangents AP and AQ are drawn to a circle with centre O from an external point A, then
$\angle$PAQ= 2$\angle$OPQ= 2$\angle$OQP

Given : $\angle$PAQ = ${50}^{\circ }$
so, $\angle$OPQ = $\frac{\angle PAQ}{2}$
$\Rightarrow$ $\angle$OPQ = $\frac{{50}^{\circ }}{2}$
$\Rightarrow$ $\angle$OPQ = ${25}^{\circ }$