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Prove that $\angle AMC=\angle BND$ and $\angle ANC=\angle BMD$

Source: Moldova TST 1996

August 8, 2023

geometry

Problem Statement

Circles

S_1{}

and

S_2{}

intersect in

M{}

and

N{}

. Line

l

intersects the circles in points

A,B\in S_1

and

C,D\in S_2

. Prove that

\angle AMC=\angle BND

and

\angle ANC=\angle BMD

if the order of points on line

l

is: a) A,C,B,D; b)

A,C,D,B.