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An inequality in right angled triangle

Source: Polish Junior Olympiad 2021 Final Round Problem 2, https://omj.edu.pl

March 21, 2021
inequalitiesgeometryTriangle Geometry

Problem Statement

Point MM is the midpoint of the hypotenuse ABAB of a right angled triangle ABCABC. Points PP and QQ lie on segments AMAM and MBMB respectively and PQ=CQPQ=CQ. Prove that AP≤2⋅MQAP\leq 2\cdot MQ.
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