2020 CIME I Problems/Problem 11

Problem 11

An $excircle$ of a triangle is a circle tangent to one of the sides of the triangle and the extensions of the other two sides. Let $ABC$ be a triangle with $\angle ACB = 90$ and let $r_A, r_B, r_C$ denote the radii of the excircles opposite to $A, B, C$, respectively. If $r_A=9$ and $r_B=11$, then $r_C$ can be expressed in the form $m+\sqrt{n}$, where $m$ and $n$ are positive integers and $n$ isn't divisible by the square of any prime. Find $m+n$.


This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

2020 CIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All CIME Problems and Solutions

The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions. AMC logo.png