2023 AIME I Problems/Problem 12

Problem 12

Let $ABC$ be an equilateral triangle with side length $55$ . Points $D$ , $E$ , and $F$ lie on sides $BC$ , $CA$ , and $AB$ , respectively, such that $BD=7$ , $CE=30$ , and $AF=40$ . A unique point $P$ inside $\triangle ABC$ has the property that $\measuredangle AEP=\measuredangle BFP=\measuredangle CDP.$ Find $\tan^{2}\measuredangle AEP$ .

Solution

Miquel point and law of cosines, answer should be 75

2023 AIME I (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2023 AIME I Problems/Problem 12

Problem 12

Solution

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