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center or rectanglie lies on MN - All-Russian MO 1997 Regional (R4) 10.2

Source:

September 24, 2024

geometryrectanglecollinear

Problem Statement

Circles

S_1

and

S_2

intersect at points

M

and

N

. Prove that if vertices

A

and

C

of some rectangle

ABCD

lie on the circle

S_1

, and the vertices

B

and

D

lie on the circle

S_2

, then the point of intersection of its diagonals lies on the line

MN