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area chasing, area of ABE is geometric mean of areas of triangles ABC, ABH

Source: CRMO 2012 region 5 p4 Mumbai

September 30, 2018
geometryarea of a triangleareasorthocenter

Problem Statement

HH is the orthocentre of an acute–angled triangle ABCABC. A point EE is taken on the line segment CHCH such that ABEABE is a right–angled triangle. Prove that the area of the triangle ABEABE is the geometric mean of the areas of triangles ABCABC and ABHABH.
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