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 ?
Answer & explanation
Correct answer: option 2
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°