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Prove that B is the incenter of DEC’

Source: 2023 Thailand Online MO P8

February 12, 2023

geometry

Problem Statement

Let

ABC

be an acute triangle with

AB<AC

. Let

M

be the midpoint of

BC

and

E

be the foot of altitude from

B

to

AC

. The point

C'

is the reflection of

C

across

AM

. The point

D

not equal to

C

is placed on line

BC

such that

AD=AC

. Prove that

B

is the incenter of triangle

DEC'

.

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