Question

PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then
$\angle OPR:\angle OPQ$ =.

• A. $2:1$
• B. $1:1$
• C. $1:2$
• D. $4:1$

Answer 1

The correct option is B $1:1$


Join the points OP, OQ and OR.
$\text{In}△OPQ\text{and}△OPR,OP=OP\text{(common side)}OQ=OR\text{(radii of the same circle)}\angle OQP=\angle ORP={90}^{\circ }\text{(Tangent is perpendicular to the}\text{radius)}\therefore \Delta OQP\cong \Delta ORP\text{(RHS congruency)}$

$\text{Hence,}\angle OPQ=\angle OPR\left(CPCT\right)$
$\Rightarrow \frac{\angle OPR}{\angle OPQ}=\frac{1}{1}\Rightarrow \angle OPR:\angle OPQ=1:1$