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Ecuador Juniors
2017 Ecuador Juniors
3
3
Part of
2017 Ecuador Juniors
Problems
(1)
CD _|_ EO if AB=AC, O circumcenter, AD=//DB. E centroid ACD
Source: 2017 Ecuador Juniors (OMEC) L2 p3
10/25/2022
Given an isosceles triangle
A
B
C
ABC
A
BC
with
A
B
=
A
C
AB = AC
A
B
=
A
C
. Let
O
O
O
be the circumcenter of
A
B
C
ABC
A
BC
,
D
D
D
the midpoint of
A
B
AB
A
B
and
E
E
E
the centroid of
A
C
D
ACD
A
C
D
. Prove that
C
D
⊥
E
O
CD \perp EO
C
D
⊥
EO
.
geometry
perpendicular
isosceles