Question

If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of ${80}^o$, then $\angle POA$ is equal to.

• A. ${50}^o$
• B. ${60}^o$
• C. ${70}^o$
• D. ${80}^o$

Answer 1

The correct option is A ${50}^o$

Given: $\angle APB={80}^{\circ }$

As we know that sum of $\angle APB+\angle AOB={180}^{\circ }$ (Using Property)

$\angle AOB={100}^{\circ }$

$\Delta$ $AOP$ $\simeq$ $\Delta$$BOP$ by SSS congruency criteria.
$AO=BO$ (Radius of circle)
$PO=PO$ (common side of triangle)
$AP=BP$ (tangents form an external point)

$\angle AOP=\angle BOP$ (CPCT )

$\angle POA+\angle POB=\angle AOB={100}^{\circ }$
$\angle POA={50}^{\circ }$