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JBMO Shortlist 2023 G1

Source: JBMO Shortlist 2023, G1

June 28, 2024
JBMOJBMO Shortlistgeometry

Problem Statement

Let ABCABC be a triangle with circumcentre OO and circumcircle Ω\Omega. Γ\Gamma is the circle passing through O,BO,B and tangent to ABAB at BB. Let Γ\Gamma intersect Ω\Omega a second time at P≠BP \neq B. The circle passing through P,CP,C and tangent to ACAC at CC intersects with Γ\Gamma at MM. Prove that ∣MP∣=∣MC∣|MP|=|MC|.
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