Question

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is

• A. 1:1
• B. 2:1
• C. 3:1
• D. 4:1

Answer 1

The correct option is A

1:1

Join the points OP,OQ and OR.
Now, in triangles OPQ and OPR,
OP = OP (common side)
OQ = OR (radii)
$\angle OQP=\angle ORP={90}^{\circ }$ (Tangent is perpendicular to the radius)
Hence,
$\Delta OQP\cong \Delta ORP$ (RHS congruency)
Hence,
$\angle OPQ=\angle OPR\left(CPCT\right)$
So,
$\frac{\angle OPR}{\angle OPQ}=\frac{1}{1}$