MathDB
Neat Geometric Inequality

Source: Tuymaada 2021 Senior P7

July 28, 2021
geometric inequalityinequalitiesgeometry

Problem Statement

An acute triangle ABCABC is given, AC≠BCAC \not= BC. The altitudes drawn from AA and BB meet at HH and intersect the external bisector of the angle CC at YY and XX respectively. The external bisector of the angle AHBAHB meets the segments AXAX and BYBY at PP and QQ respectively. If PX=QYPX = QY, prove that AP+BQ≥2CHAP + BQ \ge 2CH.
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