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CHMMC problems
2015 CHMMC (Fall)
7
2015 Fall Team #7
2015 Fall Team #7
Source:
March 26, 2022
geometry
Problem Statement
Let
I
I
I
be the incenter and let
Γ
\Gamma
Γ
be the incircle of
△
A
B
C
\vartriangle ABC
△
A
BC
, and let
P
=
Γ
∩
B
C
P = \Gamma \cap BC
P
=
Γ
∩
BC
. Let
Q
Q
Q
denote the intersection of
Γ
\Gamma
Γ
and the line passing through
P
P
P
parallel to
A
I
AI
A
I
. Let
ℓ
\ell
ℓ
be the tangent line to
Γ
\Gamma
Γ
at
Q
Q
Q
and let
ℓ
∩
A
B
=
S
\ell \cap AB = S
ℓ
∩
A
B
=
S
,
ℓ
∩
A
C
=
R
\ell \cap AC = R
ℓ
∩
A
C
=
R
. If
A
B
=
7
AB = 7
A
B
=
7
,
B
C
=
6
BC = 6
BC
=
6
,
A
C
=
5
AC = 5
A
C
=
5
, what is
R
S
RS
RS
?
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