MathDB

5

Part of 2010 Costa Rica - Final Round

Problems(1)

Trisected angle

Source: Costa Rica National Olympiad, Final Round, Problem 5

10/14/2011
Let C1C_1 be a circle with center OO and let BB and CC be points in C1C_1 such that BOCBOC is an equilateral triangle. Let DD be the midpoint of the minor arc BCBC of C1C_1. Let C2C_2 be the circle with center CC that passes through BB and OO. Let EE be the second intersection of C1C_1 and C2C_2. The parallel to DEDE through BB intersects C1C_1 for second time in AA. Let C3C_3 be the circumcircle of triangle AOCAOC. The second intersection of C2C_2 and C3C_3 is FF. Show that BEBE and BFBF trisect the angle ∠ABC\angle ABC.
geometrycircumcirclegeometric transformationreflectiongeometry unsolved