{"status": "success", "data": {"description_md": "In triangle $ABC, AB=\\sqrt{30}, AC=\\sqrt{6},$ and $BC=\\sqrt{15}.$ There is a point $D$ for which $\\overline{AD}$ bisects $\\overline{BC}$ and $\\angle ADB$ is a right angle. The ratio $$ \\frac{\\text{Area}(\\triangle ADB)}{\\text{Area}(\\triangle ABC)} $$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\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": "

In triangle ABC, AB=\\sqrt{30}, AC=\\sqrt{6}, and BC=\\sqrt{15}. There is a point D for which \\overline{AD} bisects \\overline{BC} and \\angle ADB is a right angle. The ratio \\frac{\\text{Area}(\\triangle ADB)}{\\text{Area}(\\triangle ABC)} can be written in the form m/n, where m and n are relatively prime positive integers. Find m+n.

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": "1996 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/96_aime_p14", "prev": "/problem/96_aime_p12"}}