AB is a diameter of a circle with centre O. The tangent at a point C on the circle and AB, when produced, meet at the point P. If ∠APC = 38°, then what is the measure of ∠PCB?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 26°
Calculations:
In △OCP, we have
⇒ ∠OCP + ∠OPC + ∠COP = 180
⇒ ∠COP = 180 - 90 - 38 = 52
We know that, ∠BCO = ∠CBO (angle opposite to equal sides)
△BOC is an isosceles triangle
⇒ ∠BCO + ∠CBO + ∠COB = 180
∠BCO = (180 - 52)/2 = 64
We know that, ∠PCB = 90 - ∠BCO
⇒ ∠PCB = 90 - 64 = 26