Question

In the given figure, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 56°, then calculate ∠QOR. [1 mark]

Answer 1

Step 1:

Since PR and PQ are tangents, they are perpendicular to radii OR and OQ.

Writing sum of all angles in Quadrilateral PQOR.
Hence,

∠QPR + ∠PQO + ∠PRO + ∠QOR = 360° [0.5 marks]

Step 2:

Placing the values of given angles to find the ∠QOR.

56° + 90° + 90° + ∠QOR = 360°

∠QOR = 360° - (56° + 90° + 90°)

∠QOR = 360° - 226°

∠QOR = 124° [0.5 marks]