MathDB
2023 Fall LMT Team #12 excircle

Source:

February 4, 2024
geometry

Problem Statement

In triangle ABCABC with AB=7AB = 7, AC=8AC = 8, and BC=9BC = 9, the AA-excircle is tangent to BCBC at point DD and also tangent to lines ABAB and ACAC at points and FF, respectively. Find [DEF][DEF]. (The AA-excircle is the circle tangent to segment BCBC and the extensions of rays ABAB and ACAC. Also, [XYZ][XY Z] denotes the area of triangle XYZXY Z.)
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