MathDB

Circles

S_1

and

S_2

intersect at points

M

and

N

. Through point

A

of circle

S_1

, draw straight lines

AM

and

AN

intersecting

S_2

at points

B

and

C

, and through point

D

of circle

S_2

, draw straight lines

DM

and

DN

intersecting

S_1

at points

E

and

F

, and

A

E

F

lie along one side of line

MN

, and

D

B

C

lie on the other side (see figure). Prove that if

AB = DE

, then points

A

F

C

and

D

lie on the same circle, the position of the center of which does not depend on choosing points

A

and

D

. https://cdn.artofproblemsolving.com/attachments/7/0/d1f9c2f39352e2b39e55bd2538677073618ef9.png

Problem Statement