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2010 CHMMC Winter Tiebreaker 2 - 6 AE + 7 BG + 9 CI

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March 1, 2024
geometryCHMMC

Problem Statement

In the following diagram, points E,F,G,H,IE, F, G, H, I, and JJ lie on a circle. The triangle ABCABC has side lengths AB=6AB = 6, BC=7BC = 7, and CA=9CA = 9. The three chords have lengths EF=12EF = 12, GH=15GH = 15, and IJ=16IJ = 16. Compute 6⋅AE+7⋅BG+9⋅CI6 \cdot AE + 7 \cdot BG + 9 \cdot CI.
https://cdn.artofproblemsolving.com/attachments/2/7/661b3d6a0f0baac0cd3b8d57c4cd4c62eeab46.png
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