MathDB

Iran National Math Olympiad-Day 2-Problem 5

Source:

April 30, 2010

geometrycircumcircletrigonometryvectorangle bisectorIran

Problem Statement

In triangle

ABC

we havev

\angle A=\frac{\pi}{3}

. Construct

E

and

F

on continue of

AB

and

AC

respectively such that

BE=CF=BC

. Suppose that

EF

meets circumcircle of

\triangle ACE

K

. (

K\not \equiv E

). Prove that

K

is on the bisector of

\angle A