Question

If PQ and PR are tangents to a circle with centre 'O' from an external point P, then sum of $\angle$ PQO and $\angle$ PRO is____.

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${270}^{\circ }$
• D. can't be determined.

Answer 1

The correct option is B ${180}^{\circ }$

Join centre 'O' with 'Q' and 'O' with 'R' as shown in figure.

By Theorem- Tangents at any point to a circle is perpendicular to the radius through the point of contact.
$\because$ OQ is radius and PQ is a tangent and OR is radius and PR is a tangent.
$\therefore$ OQ $\perp$ PQ and OR $\perp$ PR.
$\Rightarrow$ $\angle$ PQO = ${90}^{\circ }$ and $\angle$ PRO = ${90}^{\circ }$.
Hence, $\angle$ PQO + $\angle$ PRO = ${180}^{\circ }$.