MathDB

F,C,H are collinear

Source:

November 9, 2010

geometrygeometric transformationreflectionpower of a pointgeometry unsolved

Problem Statement

The circle

\Gamma

and the line

\ell

have no common points. Let

AB

be the diameter of

\Gamma

perpendicular to

\ell

, with

B

closer to

\ell

than

A

. An arbitrary point

C\not= A

,

B

is chosen on

E

. The line

AC

intersects

BE

at

D

. The line

DE

is tangent to

\Gamma

at

E

, with

B

and

E

on the same side of

AC

. Let

BE

intersect

\ell

at

F

, and let

AF

intersect

\Gamma

at

G\not= A

. Let

H

be the reflection of

G

in

AB

. Show that

F,C

, and

H

are collinear.

Back to Problems View on AoPS