{"status": "success", "data": {"description_md": "Let $\\triangle{PQR}$ be a right triangle with $PQ=90$, $PR=120$, and $QR=150$. Let $C_{1}$ be the inscribed circle. Construct $\\overline{ST}$ with $S$ on $\\overline{PR}$ and $T$ on $\\overline{QR}$, such that $\\overline{ST}$ is perpendicular to $\\overline{PR}$ and tangent to $C_{1}$. Construct $\\overline{UV}$ with $U$ on $\\overline{PQ}$ and $V$ on $\\overline{QR}$ such that $\\overline{UV}$ is perpendicular to $\\overline{PQ}$ and tangent to $C_{1}$. Let $C_{2}$ be the inscribed circle of $\\triangle{RST}$ and $C_{3}$ the inscribed circle of $\\triangle{QUV}$. The distance between the centers of $C_{2}$ and $C_{3}$ can be written as $\\sqrt{10n}$. What is $n$?\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": "

Let \\triangle{PQR} be a right triangle with PQ=90, PR=120, and QR=150. Let C_{1} be the inscribed circle. Construct \\overline{ST} with S on \\overline{PR} and T on \\overline{QR}, such that \\overline{ST} is perpendicular to \\overline{PR} and tangent to C_{1}. Construct \\overline{UV} with U on \\overline{PQ} and V on \\overline{QR} such that \\overline{UV} is perpendicular to \\overline{PQ} and tangent to C_{1}. Let C_{2} be the inscribed circle of \\triangle{RST} and C_{3} the inscribed circle of \\triangle{QUV}. The distance between the centers of C_{2} and C_{3} can be written as \\sqrt{10n}. What is 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": 4, "problem_name": "2001 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_II_p08", "prev": "/problem/01_aime_II_p06"}}