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2015 JHMT Geometry #5

Source:

September 5, 2023
geometry

Problem Statement

Points ABCDEFABCDEF are evenly spaced on a unit circle and line segments ADAD, DFDF, FBFB, BEBE, ECEC, CACA are drawn. The line segments intersect each other at seven points inside the circle. Denote these intersections p1p_1, p2p_2, ......,p7p_7, where p7p_7 is the center of the circle. What is the area of the 1212-sided shape Ap1Bp2Cp3Dp4Ep5Fp6A_{p_1}B_{p_2}C_{p_3}D_{p_4}E_{p_5}F_{p_6}? https://cdn.artofproblemsolving.com/attachments/9/2/645b3c31b0bb7f81d0c0b86e13b27ec5b32864.png
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