Problem

Holiday Contest 2025 - Guts Round - Set 7 Problem 1

A rhombus with diagonals length $6$ and $8$ has a circle $O$ inscribed in it. Two circles $A$ and $B$ of different radii length are both internally tangent to the rhombus at two points and also externally tangent to circle $O$ at one point. The sum of the radii of circles $A$ and $B$ can be expressed as $\frac{m}{n}$ . Compute $m+n$ .

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Category: Holiday Contest Guts Round
Points: 5
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