In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If ∠POQ = 54º, then the measure of ∠PCA is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 63º
∠APB = 90°.
∠PAQ = 1/2 × 54° = 27° ( Angle subtended by the arc at circumference will be half of the angle subtended at the centre).
Now in APC,
90 + 27 + ∠PCA = 180°.
∠PCA = 63°.