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2011 Princeton University Math Competition
A4
A4
Part of
2011 Princeton University Math Competition
Problems
(2)
2011 PUMaC Algebra A4
Source:
9/24/2019
Suppose the polynomial
x
3
ā
x
2
+
b
x
+
c
x^3 - x^2 + bx + c
x
3
ā
x
2
+
b
x
+
c
has real roots
a
,
b
,
c
a, b, c
a
,
b
,
c
. What is the square of the minimum value of
a
b
c
abc
ab
c
?
algebra
2011 PUMaC Geometry A4
Source:
9/24/2019
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
15
,
B
C
=
17
AB = 15, BC = 17
A
B
=
15
,
BC
=
17
,
C
A
=
21
CA = 21
C
A
=
21
, and incenter
I
I
I
. If the circumcircle of triangle
I
B
C
IBC
I
BC
intersects side
A
C
AC
A
C
again at
P
P
P
, find
C
P
CP
CP
.
geometry