MathDB

2

Part of 2021 Polish Junior MO Finals

Problems(1)

An inequality in right angled triangle

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

3/21/2021
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.
inequalitiesgeometryTriangle Geometry