MathDB

Let

ABC

be a triangle and

X,Y,Z

be the tangency points of its inscribed circle with the sides

BC, CA, AB

, respectively. Suppose that

C_1, C_2, C_3

are circle with chords

YZ, ZX, XY

, respectively, such that

C_1

and

C_2

intersect on the line

CZ

and that

C_1

and

C_3

intersect on the line

BY

. Suppose that

C_1

intersects the chords

XY

and

ZX

J

and

M

, respectively; that

C_2

intersects the chords

YZ

and

XY

L

and

I

, respectively; and that

C_3

intersects the chords

YZ

and

ZX

K

and

N

, respectively. Show that

I, J, K, L, M, N

lie on the same circle.

Problem Statement