Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
If in a
Δ
A
B
C
\Delta ABC
Δ
A
B
C
,
a
cos
A
+
b
cos
B
+
c
cos
C
a
sin
B
+
b
sin
C
+
c
sin
A
=
a
+
b
+
c
9
R
\frac{a \cos A + b \cos B + c \cos C}{a \sin B + b \sin C + c \sin A} = \frac{a+b+c}{9R}
a
s
i
n
B
+
b
s
i
n
C
+
c
s
i
n
A
a
c
o
s
A
+
b
c
o
s
B
+
c
c
o
s
C
=
9
R
a
+
b
+
c
, then prove that
Δ
\Delta
Δ
is equilateral.
Browse the problem library