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 ?
Answer & explanation
Correct answer: option 1
∠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°