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5
Math Prize 2011 Problem 5
Math Prize 2011 Problem 5
Source:
September 19, 2011
Pythagorean Theorem
geometry
Problem Statement
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with
A
B
=
3
AB = 3
A
B
=
3
,
B
C
=
4
BC = 4
BC
=
4
, and
A
C
=
5
AC = 5
A
C
=
5
. Let
I
I
I
be the center of the circle inscribed in
△
A
B
C
\triangle ABC
△
A
BC
. What is the product of
A
I
AI
A
I
,
B
I
BI
B
I
, and
C
I
CI
C
I
?
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