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2023 MOAA Gunga P24

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October 15, 2023
MOAA 2023

Problem Statement

Circle ω\omega is inscribed in acute triangle ABCABC. Let II denote the center of ω\omega, and let D,E,FD,E,F be the points of tangency of ω\omega with BC,CA,ABBC, CA, AB respectively. Let MM be the midpoint of BCBC, and PP be the intersection of the line through II perpendicular to AMAM and line EFEF. Suppose that AP=9AP=9, EC=2EAEC=2EA, and BD=3BD=3. Find the sum of all possible perimeters of △ABC\triangle ABC.
Proposed by Harry Kim
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