{"status": "success", "data": {"description_md": "Let $ABCDE$ be a regular pentagon. Let there be a point $P$ in the triangle $ACD$ such that $P$, $D$, and $B$ are collinear. We extend $AP$ to intersect side $CD$ at point $F$, where $\\frac{DF}{FC} = \\frac{1}{2}$. We extend $CP$ to intersect side $ED$ at point $G$ and segment $AD$ at point $H$. Then, the ratio $\\frac{HD}{AH}$ can be written as $\\frac{\\sqrt{p} - q}{r}$, where $p$ is square free. Find $p+q+r$.", "description_html": "

Let ABCDE be a regular pentagon. Let there be a point P in the triangle ACD such that P, D, and B are collinear. We extend AP to intersect side CD at point F, where \\frac{DF}{FC} = \\frac{1}{2}. We extend CP to intersect side ED at point G and segment AD at point H. Then, the ratio \\frac{HD}{AH} can be written as \\frac{\\sqrt{p} - q}{r}, where p is square free. Find p+q+r.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "AMC Practice #1 - Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/amc1-p12", "prev": "/problem/amc1-p10"}}