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Putnam
1966 Putnam
A2
Putnam 1966 A2
Putnam 1966 A2
Source:
April 6, 2022
college contests
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be the lengths of the sides of a triangle, let
p
=
(
a
+
b
+
c
)
/
2
p=(a+b+c)/2
p
=
(
a
+
b
+
c
)
/2
, and
r
r
r
be the radius of the inscribed circle. Show that
1
(
p
−
a
)
2
+
1
(
p
−
b
)
2
+
1
(
p
−
c
)
2
≥
1
r
2
.
\frac{1}{(p-a)^2}+ \frac{1}{(p-b)^2}+\frac{1}{(p-c)^2} \geq \frac{1}{r^2}.
(
p
−
a
)
2
1
+
(
p
−
b
)
2
1
+
(
p
−
c
)
2
1
≥
r
2
1
.
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