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Let AXYZB be a convex pentagon inscribed in a semicircle of diameter AB. Denote by P,Q,R,S the feet of the perpendiculars from Y onto lines AX, BX, AZ, BZ respectively. Prove that the acute angle formed by lines PQ and RS is half the size of \(\angle XOZ\), where O is the midpoint of segment AB.

 Jan 13, 2024

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