{"status": "success", "data": {"description_md": "Let $ABCD$ be a convex quadrilateral with $AB=CD=10$, $BC=14$, and $AD=2\\sqrt{65}$. Assume that the diagonals of $ABCD$ intersect at point $P$, and that the sum of the areas of $\\triangle APB$ and $\\triangle CPD$ equals the sum of the areas of $\\triangle BPC$ and $\\triangle APD$. Find the area of quadrilateral $ABCD$.\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": "<p>Let <span class=\"katex--inline\">ABCD</span> be a convex quadrilateral with <span class=\"katex--inline\">AB=CD=10</span>, <span class=\"katex--inline\">BC=14</span>, and <span class=\"katex--inline\">AD=2\\sqrt{65}</span>. Assume that the diagonals of <span class=\"katex--inline\">ABCD</span> intersect at point <span class=\"katex--inline\">P</span>, and that the sum of the areas of <span class=\"katex--inline\">\\triangle APB</span> and <span class=\"katex--inline\">\\triangle CPD</span> equals the sum of the areas of <span class=\"katex--inline\">\\triangle BPC</span> and <span class=\"katex--inline\">\\triangle APD</span>. Find the area of quadrilateral <span class=\"katex--inline\">ABCD</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2018 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_II_p13", "prev": "/problem/18_aime_II_p11"}}