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2023 HMIC
P3
P3
Part of
2023 HMIC
Problems
(1)
invert your expectations pt.2
Source: 2023 HMIC 3
4/25/2023
Triangle
A
B
C
ABC
A
BC
has incircle
ω
\omega
ω
and
A
A
A
-excircle
ω
A
.
\omega_A.
ω
A
.
Circle
γ
B
\gamma_B
γ
B
passes through
B
B
B
and is externally tangent to
ω
\omega
ω
and
ω
A
.
\omega_A.
ω
A
.
Circle
γ
C
\gamma_C
γ
C
passes through
C
C
C
and is externally tangent to
ω
\omega
ω
and
ω
A
.
\omega_A.
ω
A
.
If
γ
B
\gamma_B
γ
B
intersects line
B
C
BC
BC
again at
D
,
D,
D
,
and
γ
C
\gamma_C
γ
C
intersects line
B
C
BC
BC
again at
E
,
E,
E
,
prove that
B
D
=
E
C
.
BD=EC.
B
D
=
EC
.
Inversion
geometry
HMIC