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2022 Iberoamerican
1
1
Part of
2022 Iberoamerican
Problems
(1)
Equilateral triangle geo
Source: Iberoamerican 2022, Day 1, P1
9/29/2022
Given is an equilateral triangle
A
B
C
ABC
A
BC
with circumcenter
O
O
O
. Let
D
D
D
be a point on to minor arc
B
C
BC
BC
of its circumcircle such that
D
B
>
D
C
DB>DC
D
B
>
D
C
. The perpendicular bisector of
O
D
OD
O
D
meets the circumcircle at
E
,
F
E, F
E
,
F
, with
E
E
E
lying on the minor arc
B
C
BC
BC
. The lines
B
E
BE
BE
and
C
F
CF
CF
meet at
P
P
P
. Prove that
P
D
⊥
B
C
PD \perp BC
P
D
⊥
BC
.
geometry