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Trisected angle

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

October 14, 2011

geometrycircumcirclegeometric transformationreflectiongeometry unsolved

Problem Statement

Let

D

be a circle with center

O

and let

B

and

C

be points in

C_1

such that

BOC

is an equilateral triangle. Let

D

be the midpoint of the minor arc

BC

of

C_1

. Let

C_2

be the circle with center

C

that passes through

B

and

C_1

. Let

E

be the second intersection of

C_1

and

C_2

. The parallel to

DE

through

B

intersects

C_1

for second time in

A

. Let

C_3

be the circumcircle of triangle

AOC

. The second intersection of

C_2

and

C_3

is

F

. Show that

BE

and

BF

trisect the angle

\angle ABC

.

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