2019 CIME I Problems/Problem 14

Let $ABC$ be a triangle with circumcenter $O$ and incenter $I$ such that the lengths of the three segments $AB$ , $BC$ , and $CA$ form an increasing arithmetic progression in this order. If $AO=60$ and $AI=58$ , then the distance from $A$ to $BC$ can be expressed as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

2019 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2019 CIME I Problems/Problem 14