2018 AIME I Problems/Problem 13
Problem
Let have side lengths , , and . Point lies in the interior of , and points and are the incenters of and , respectively. Find the minimum possible area of as varies along .
Solution
First note that is a constant not depending on , so by it suffices to minimize . Let , , , and . Remark that Applying the Law of Sines to gives Analogously one can derive , and so with equality when , that is, when is the foot of the perpendicular from to . In this case the desired area is . To make this feasible to compute, note that Applying similar logic to and and simplifying yields a final answer of
See Also
2018 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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