MathDB

German angle bisecting problem

Source: Germany Bundeswettbewerb Mathematik 2007, Round 1, Problem 3

July 18, 2008

geometrycircumcircletrigonometrypower of a pointradical axisgeometry unsolved

Problem Statement

In triangle

ABC

points

E

and

F

lie on sides

AC

and

BC

such that segments

AE

and

BF

have equal length, and circles formed by

A,C,F

and by

B,C,E,

respectively, intersect at point

C

and another point

D.

Prove that that the line

CD

bisects

\angle ACB.