{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be an equilateral triangle with side length $55$. Points $D$, $E$, and $F$ lie on sides $\\overline{BC}$, $\\overline{CA}$, and $\\overline{AB}$, respectively, with $BD=7$, $CE=30$, and $AF=40$. A unique point $P$ inside $\\triangle ABC$ has the property that $$\\angle AEP=\\angle BFP=\\angle CDP. $$Find $\\tan^{2}\\left(\\angle AEP\\right)$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2023 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_I_p13", "prev": "/problem/23_aime_I_p11"}}