HMMT 2014 U15
- Guts
- Answer
Given a regular pentagon of area 1, a pivot line is a line not passing through any of the pentagon's vertices such that there are 3 vertices of the pentagon on one side of the line and 2 on the other. A pivot point is a point inside the pentagon with only finitely many non-pivot lines passing through it. Find the area of the region of pivot points.
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{1}{2}(7-3 \sqrt{5})
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