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BP=1/3 AB wanted, semicircle - 1993 Cono Sur Shortlist G11

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October 24, 2021
geometryequal segmentssemicircle

Problem Statement

Let Γ\Gamma be a semicircle with center OO and diameter ABAB. DD is the midpoint of arc ABAB. On the ray ODOD, we take EE such that OE=BDOE = BD. BEBE intersects the semicircle at FF and P P is the point on ABAB such that FPFP is perpendicular to ABAB. Prove that BP=13ABBP=\frac13 AB.
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