2020 CIME II Problems/Problem 1

Problem

Let $ABC$ be a triangle. The bisector of $\angle ABC$ intersects $\overline{AC}$ at $E$ , and the bisector of $\angle ACB$ intersects $\overline{AB}$ at $F$ . If $BF=1$ , $CE=2$ , and $BC=3$ , then the perimeter of $\triangle ABC$ can be expressed in the form $\tfrac mn$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

2020 CIME II (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
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2020 CIME II Problems/Problem 1

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