In 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 = 52°, then what is the measure of ∠PCA ?

64°

∠PAQ = \(\frac{1}{2}\) ∠POQ       [Produced by same chord]

∠PAQ = 26°

∠APB = 90°   (angle in semi circle)

∴  ∠ACP in ΔAPC

∠APC + ∠PAC + ∠ACP = 180°

90° + 26° + ∠ACP = 180°

                  ∠ACP = 64°