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Show that DE and AC are perpendicular

Source: Moldova TST 2020

March 8, 2020

geometry

Problem Statement

In

\Delta ABC

the angles

ABC

and

ACB

are acute. Let

M

be the midpoint of

AB

. Point

B

is on the half-line

CD

such that

B \in (CD)

and

\angle DAB= \angle BCM

. Perpendicular from

B

to line

CD

intersects the line bisector of

AB

in

E

. Prove that

DE

and

AC

are perpendicular.

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