MathDB

K is the circumcenter of triangle AOC

Source: All-Russian MO 2000

December 30, 2012

geometrycircumcircleparallelogramAsymptoteperpendicular bisector

Problem Statement

Let

O

be the center of the circumcircle

\omega

of an acute-angle triangle

ABC

. A circle

\omega_1

with center

K

passes through

A

O

C

and intersects

AB

M

and

BC

N

. Point

L

is symmetric to

K

with respect to line

NM

. Prove that

BL \perp AC