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MN = AE +AF, 2 intersecting circles

Source: All-Russian MO 1995 Regional (R4) 11.7

August 26, 2024

geometryequal segments

Problem Statement

Circles

S_1

and

S_2

with centers

O_1

and

O_2

respectively intersect at

A

and

B

. Ray

O_1B

meets

S_2

again at

F

, and ray

O_2B

meets

S_1

again at

E

. The line through

B

parallel to

EF

intersects

S_1

and

S_2

again at

M

and

N

, respectively. Prove that

MN = AE +AF

.

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