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Let $ABC$ be a right triangle, right at $B$

Source: May Olimpiad 2020 L2 P4

November 27, 2020
geometry

Problem Statement

Let ABCABC be a right triangle, right at BB, and let MM be the midpoint of the side BCBC. Let PP be the point in bisector of the angle ∠BAC \angle BAC such that PMPM is perpendicular to BC(PBC (P is outside the triangle ABCABC). Determine the triangle area ABCABC if PM=1PM = 1 and MC=5MC = 5.
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