MathDB

concurrent lines, altitudes related, from Sharygin 2007

Source: Sharygin 2007 Final 10.2

April 30, 2019

geometryaltitudesCircumcenterconcurrentconcurrency

Problem Statement

Points

A', B', C'

are the feet of the altitudes

AA', BB'

and

CC'

of an acute triangle

ABC

. A circle with center

B

and radius

BB'

meets line

A'C'

at points

K

and

L

(points

K

and

A

are on the same side of line

BB'

). Prove that the intersection point of lines

AK

and

CL

belongs to line

BO

(

O

is the circumcenter of triangle

ABC