In the following figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.

Join OP and OQ
Given ∠PRQ = 120°
∴ ∠POQ = 60° (supplementary angles)
Also, we have PR = RQ (equal tangents) and ∠OPR = 90° (radii is perpendicular to tangent)
Now, PR/OR = cos 60° = 1/2 (∠ROP = 30° and ∠PRO = 60°)
⇒ OR = 2PR
⇒ OR = PR + RQ
Hence proved