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2020 Taiwan APMO Preliminary Problem 7

Source: 2020 Taiwan APMO Preliminary

July 23, 2020
geometry

Problem Statement

[XYZXYZ] denotes the area of △XYZ\triangle XYZ We have a △ABC\triangle ABC,BC=6,CA=7,AB=8BC=6,CA=7,AB=8 (1)If OO is the circumcenter of △ABC\triangle ABC, find [OBCOBC]:[OCAOCA]:[OABOAB] (2)If HH is the orthocenter of △ABC\triangle ABC, find [HBCHBC]:[HCAHCA]:[HABHAB]
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