ΔABC is drawn in a circle such that AC = BC and ∠BAC = 65°. From points B and C two tangents are drawn which intersect at point P. What is the measure of ∠BPC ?

50°

We know that,

Angle subtended by arc at centre is twice the angle subtended by arc at circumference.

AC = BC

∠BAC = 65°.

Here, Radius is perpendicular to tangent. 

So, ∠BOC = 2× ∠BAC = 2 × 65° = 130° 

Also, Radius is perpendicular to tangent 

= ∠OBP = ∠OCP = 90°

= ∠BOC + ∠BPC + ∠OBP + ∠OCP = 360°

= ∠BPC = 360° - 130° - 90° - 90° = 50°