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 = 54°, then the measure of ∠PCA is:

Answer: Option A

Solution

Answer: Option A

Solution:

2α + 2β + 54° = 180°
2(α + β) = 126°
α + β = 63°
∠PCA = ∠CAB + ∠CBA
= α + β
= 63°