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2022 LMT Spring Accuracy Problem 8

Source:

September 29, 2023
geometry

Problem Statement

A ray originating at point PP intersects a circle with center OO at points AA and BB, with PB>PAPB > PA. Segment OP‾\overline{OP} intersects the circle at point CC. Given that PA=31PA = 31, PC=17PC = 17, and ∠PBO=60o\angle PBO = 60^o, find the radius of the circle.
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