Difference between revisions of "2020 CIME I Problems/Problem 11"

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[[Category:Intermediate Geometry Problems]]
 
[[Category:Intermediate Geometry Problems]]
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Latest revision as of 16:20, 31 August 2020

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 $m+n$.

Solution

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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

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