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prove perpendicularity with equal lengths and midpoint

Source: Sharygin 2023 - P5 (Grade-8)

March 4, 2023

geometryperpendicularSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let

ABCD

be a cyclic quadrilateral. Points

E

and

F

lie on the sides

AD

and

CD

in such a way that

AE = BC

and

AB = CF

. Let

M

be the midpoint of

EF

. Prove that

\angle AMC = 90^{\circ}