Question

The radius of a circle with center O is 8cm. P is a point outside the circle. PQ and PR are the tangents drawn from P to the circle. If ∠QOR = 60° then find the lengths of PQ, PR, and OP.

Answer 1

In Δ OPQ the angles are 30°, 60°, and 90°. 

∴ The sides are in the ratio 1 : √3 : 2

∴ PQ = \(\frac{8}{\sqrt{3}}\) = PR = \(\frac{8}{\sqrt{3}}\)

OP = \(2\times \frac{8}{\sqrt{3}}=\frac{16}{\sqrt{3}}\)