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CentroAmerican
2020 Centroamerican and Caribbean Math Olympiad
4
4
Part of
2020 Centroamerican and Caribbean Math Olympiad
Problems
(1)
Easy geometry
Source: Centroamerican 2020, problem 4
10/28/2020
Consider a triangle
A
B
C
ABC
A
BC
with
B
C
>
A
C
BC>AC
BC
>
A
C
. The circle with center
C
C
C
and radius
A
C
AC
A
C
intersects the segment
B
C
BC
BC
in
D
D
D
. Let
I
I
I
be the incenter of triangle
A
B
C
ABC
A
BC
and
Γ
\Gamma
Γ
be the circle that passes through
I
I
I
and is tangent to the line
C
A
CA
C
A
at
A
A
A
. The line
A
B
AB
A
B
and
Γ
\Gamma
Γ
intersect at a point
F
F
F
with
F
≠
A
F \neq A
F
=
A
. Prove that
B
F
=
B
D
BF=BD
BF
=
B
D
.
geometry
incenter
circles