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2023 Fall LMT Speed p14 , [ACD]+[BCD]

Source:

March 2, 2024
geometry

Problem Statement

In obtuse triangle ABCABC with AB=7AB = 7, BC=20BC = 20, and CA=15C A = 15, let point DD be the foot of the altitude from CC to line ABAB. Evaluate [ACD]+[BCD][ACD]+[BCD]. (Note that [XYZ][XY Z] means the area of triangle XYZXY Z.)
Proposed by Jonathan Liu
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