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Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2010 Saudi Arabia Pre-TST
2.4
2.4
Part of
2010 Saudi Arabia Pre-TST
Problems
(1)
x^3- (a^2 + b^2 + c^2)x -2abc = 0 for quadrilateral inscribed in semicircle
Source: 2010 Saudi Arabia Pre-TST 2.4
12/28/2021
Let
A
M
N
B
AMNB
A
MNB
be a quadrilateral inscribed in a semicircle of diameter
A
B
=
x
AB = x
A
B
=
x
. Denote
A
M
=
a
AM = a
A
M
=
a
,
M
N
=
b
MN = b
MN
=
b
,
N
B
=
c
NB = c
NB
=
c
. Prove that
x
3
−
(
a
2
+
b
2
+
c
2
)
x
−
2
a
b
c
=
0
x^3- (a^2 + b^2 + c^2)x -2abc = 0
x
3
−
(
a
2
+
b
2
+
c
2
)
x
−
2
ab
c
=
0
.
semicircle
inscribed
geometry