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2018 Stanford Mathematics Tournament
10
10
Part of
2018 Stanford Mathematics Tournament
Problems
(1)
SMT 2018 Geometry #10 2 incircles
Source:
8/8/2023
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
13
AB = 13
A
B
=
13
,
A
C
=
14
AC = 14
A
C
=
14
, and
B
C
=
15
BC = 15
BC
=
15
, and let
Γ
\Gamma
Γ
be its incircle with incenter
I
I
I
. Let
D
D
D
and
E
E
E
be the points of tangency between
Γ
\Gamma
Γ
and
B
C
BC
BC
and
A
C
AC
A
C
respectively, and let
ω
\omega
ω
be the circle inscribed in
C
D
I
E
CDIE
C
D
I
E
. If
Q
Q
Q
is the intersection point between
Γ
\Gamma
Γ
and
ω
\omega
ω
and
P
P
P
is the intersection point between
C
Q
CQ
CQ
and
ω
\omega
ω
, compute the length of
P
Q
P Q
PQ
.
geometry