MathDB

B,C,G,H are chosen on the circumference of omega

Source: Itamo 2014 - p4

November 22, 2014

geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

Let

\omega

be a circle with center

A

and radius

R

. On the circumference of

\omega

four distinct points

B, C, G, H

are taken in that order in such a way that

G

lies on the extended

B

-median of the triangle

ABC

, and H lies on the extension of altitude of

ABC

from

B

. Let

X

be the intersection of the straight lines

AC

and

GH

. Show that the segment

AX

has length

2R

.

Back to Problems View on AoPS