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Circle Intersections form a Circle!

Source: OMM 2008 6

July 19, 2014

geometrycircumcirclepower of a pointradical axisgeometry unsolved

Problem Statement

The internal angle bisectors of

A

,

B

, and

C

in

\triangle ABC

concur at

I

and intersect the circumcircle of

\triangle ABC

at

CA

,

M

, and

N

, respectively. The circle with diameter

IL

intersects

BC

at

D

and

E

; the circle with diameter

IM

intersects

CA

at

F

and

G

; the circle with diameter

IN

intersects

AB

at

H

and

J

. Show that

D

,

E

,

F

,

G

,

H

, and

J

are concyclic.

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