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Fixed construction geometry problem

Source: 2022 Bulgarian Spring Math Competition, Problem 8.2

March 27, 2022

geometryangle bisectorequal lengths

Problem Statement

Let

\triangle ABC

have

AB = 1

cm,

BC = 2

cm and

AC = \sqrt{3}

cm. Points

D

,

E

and

F

lie on segments

AB

,

AC

and

BC

respectively are such that

AE = BD

and

BF = AD

. The angle bisector of

\angle BAC

intersects the circumcircle of

\triangle ADE

for the second time at

M

and the angle bisector of

\angle ABC

intersects the circumcircle of

\triangle BDF

at

N

. Determine the length of

MN

.

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