MathDB

Let point

A

be one of the intersections of circles

c

and

k

. Let

X_1

and

X_2

be arbitrary points on circle

c

. Let

Y_i

denote the intersection of line

AX_i

and circle

k

for

i=1,2

. Let

P_1

P_2

and

P_3

be arbitrary points on circle

k

, and let

O

denote the center of circle

k

. Let

K_{ij}

denote the center of circle

(X_iY_iP_j)

for

i=1,2

and

j=1,2,3

. Let

L_j

denote the center of circle

(OK_{1j}K_{2j})

for

j=1,2,3

. Prove that points

L_1

L_2

and

L_3

are collinear.
Proposed by Vilmos Molnár-Szabó, Budapest

A. 878