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Indonesia National Science Olympiad 2010 - Day 1 Problem 2

Source:

September 28, 2010

geometrycircumcircleprojective geometrygeometry unsolved

Problem Statement

Given an acute triangle

AB

with

AC>BC

and the circumcenter of triangle

ABC

is

O

. The altitude of triangle

ABC

from

C

intersects

AB

and the circumcircle at

D

and

E

, respectively. A line which passed through

O

which is parallel to

AB

intersects

AC

at

F

. Show that the line

CO

, the line which passed through

F

and perpendicular to

AC

, and the line which passed through

E

and parallel with

DO

are concurrent.
Fajar Yuliawan, Bandung

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