Library / /87 of 740

, 2018

Geometry Difficulty 4.6 AIME Prove it United States

Problem:

Square $CASH$ and regular pentagon $MONEY$ are both inscribed in a circle. Given that they do not share a vertex, how many intersections do these two polygons have?

Solution

Solution:

Pentagon $MONEY$ divides the circumference into $5$ circular arcs, and each vertex of $CASH$ lies in a different arc. Then each side of $CASH$ will intersect two sides of $MONEY$ , for a total of $8$ intersections.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.