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2010 VTRMC
Problem 4
prove side equation given angle equation
prove side equation given angle equation
Source: VTRMC 2010 P4
May 17, 2021
geometry
Triangles
Problem Statement
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with sides
a
,
b
,
c
a,b,c
a
,
b
,
c
and corresponding angles
A
,
B
,
C
A,B,C
A
,
B
,
C
(so
a
=
B
C
a=BC
a
=
BC
and
A
=
∠
B
A
C
A=\angle BAC
A
=
∠
B
A
C
etc.). Suppose that
4
A
+
3
C
=
54
0
∘
4A+3C=540^\circ
4
A
+
3
C
=
54
0
∘
. Prove that
(
a
−
b
)
2
(
a
+
b
)
=
b
c
2
(a-b)^2(a+b)=bc^2
(
a
−
b
)
2
(
a
+
b
)
=
b
c
2
.
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