MathDB
angle chase or bash

Source: 2019 AIME II #11

March 22, 2019
2019 AIME IIAIMEAIME II

Problem Statement

Triangle ABCABC has side lengths AB=7,BC=8,AB=7, BC=8, and CA=9.CA=9. Circle ω1\omega_1 passes through BB and is tangent to line ACAC at A.A. Circle ω2\omega_2 passes through CC and is tangent to line ABAB at A.A. Let KK be the intersection of circles ω1\omega_1 and ω2\omega_2 not equal to A.A. Then AK=mn,AK=\tfrac{m}{n}, where mm and nn are relatively prime positive integers. Find m+n.m+n.
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