If PT is tangent drawn from a point P to a circle touching it at T and O is the centre of the circle, then ∠ OPT + ∠ POT =

Question

Philoid · Accepted Answer

Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

Property 2: Sum of all angles of a triangle = 180°

By property 1, ∆PTO is right-angled at ∠OTP (i.e., ∠OTP = 90°).

By property 2,

∠OTP + ∠POT + ∠TPO = 180°

⇒ 90° + ∠POT + ∠TPO = 180°

⇒ ∠POT + ∠TPO = 180° - 90°

⇒ ∠POT + ∠TPO = 90°

Hence, ∠POT + ∠TPO = 90°