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2019 MOAA Team P7

Source:

January 23, 2022
number theoryteam2019

Problem Statement

Suppose ABCABC is a triangle inscribed in circle ω\omega . Let A′A' be the point on ω\omega so that AA′AA' is a diameter, and let GG be the centroid of ABCABC. Given that AB=13AB = 13, BC=14BC = 14, and CA=15CA = 15, let xx be the area of triangle AGA′AGA' . If xx can be expressed in the form m/nm/n , where m and n are relatively prime positive integers, compute 100n+m100n + m.
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