{"status": "success", "data": {"description_md": "Equilateral $\\triangle ABC$ has side length $600$. Points $P$ and $Q$ lie outside of the plane of $\\triangle ABC$ and are on the opposite sides of the plane. Furthermore, $PA=PB=PC$, and $QA=QB=QC$, and the planes of $\\triangle PAB$ and $\\triangle QAB$ form a $120^{\\circ}$ dihedral angle (The angle between the two planes). There is a point $O$ whose distance from each of $A,B,C,P$ and $Q$ is $d$. Find $d$.\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": "

Equilateral \\triangle ABC has side length 600. Points P and Q lie outside of the plane of \\triangle ABC and are on the opposite sides of the plane. Furthermore, PA=PB=PC, and QA=QB=QC, and the planes of \\triangle PAB and \\triangle QAB form a 120^{\\circ} dihedral angle (The angle between the two planes). There is a point O whose distance from each of A,B,C,P and Q is d. Find d.

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": 6, "problem_name": "2016 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p15", "prev": "/problem/16_aime_II_p13"}}