MathDB
Catcher in the Right Triangle

Source: 2017 AIME II #3

March 23, 2017
AMCAIMEAIME II

Problem Statement

A triangle has vertices A(0,0)A(0,0), B(12,0)B(12,0), and C(8,10)C(8,10). The probability that a randomly chosen point inside the triangle is closer to vertex BB than to either vertex AA or vertex CC can be written as pq\frac{p}{q}, where pp and qq are relatively prime positive integers. Find p+qp+q.