HMMT 二月 1998 · 几何 · 第 2 题
HMMT February 1998 — Geometry — Problem 2
题目详情
英文原题
Question Two . [3 points]
Anne and Lisa enter a park that hastwo concentric circular paths joinedby two radial paths, one of which is at the point where they enter. Anne goesin to the inner circle along the firstradial path, around by the shorter wayto the second radial path and outexitalong it to the exit. Walking at a the same rate, Lisa goes around the outercircle to the exit, taking the shorterenterof the two directions around the park.
They arrive at the exit at the same time. The radial paths meet at the center of the park; what is the angle between them?
解析
英文解析
- If the angle in radians is θ , then Anne travels Rθ and Lisa travels ( R − r ) + rθ + ( R − r ).
Setting these equal yields R ( θ − 2) = r ( θ − 2), so θ = 2 radians .
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