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Four points lie on the same circle

Source: BdMO 2022 Secondary P5

April 12, 2022

geometry

Problem Statement

In an acute triangle

\triangle ABC

, the midpoint of

BC

is

M

. Perpendicular lines

BE

and

CF

are drawn respectively on

AC

from

B

and on

AB

from

C

such that

E

and

F

lie on

AC

and

AB

respectively. The midpoint of

EF

is

N.

MN

intersects

AB

at

K.

Prove that, the four points

B,K,E,M

lie on the same circle.

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