In a circle with center 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 = 56°, then the measure of ∠PCA is ?

62°

∠APB = 90° (angle made by diameter)

∠PAQ = \(\frac{1}{2}\) ∠POQ = \(\frac{1}{2}\) (56°) [angle made by same chord on centre is double to the angle made by chord on circumference]

= 28°

Now in ΔAPC

∠PCA + ∠PAC + ∠CPA = 180°

∠PCA + 90° + 28° = 180°

∠PCA = 62°