Question

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 = 

A. 30° 

B. 60° 

C. 90° 

D. 180°

Answer 1

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°