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2022 CMIMC
1.7
2022 Geo Div 1 P7
2022 Geo Div 1 P7
Source:
February 28, 2022
geometry
Problem Statement
In acute
△
A
B
C
,
\triangle ABC,
△
A
BC
,
let
I
I
I
denote the incenter and suppose that line
A
I
AI
A
I
intersects segment
B
C
BC
BC
at a point
D
.
D.
D
.
Given that
A
I
=
3
,
I
D
=
2
,
AI=3, ID=2,
A
I
=
3
,
I
D
=
2
,
and
B
I
2
+
C
I
2
=
64
,
BI^2+CI^2=64,
B
I
2
+
C
I
2
=
64
,
compute
B
C
2
.
BC^2.
B
C
2
.
Proposed by Kyle Lee
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