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Byju's Answer
Standard IX
Mathematics
Basics of Geometry
In ABC, sho...
Question
In
△
A
B
C
, show that
a
c
o
s
A
+
b
c
o
s
B
+
c
c
o
s
C
a
+
b
+
c
=
r
R
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Solution
Using
a
=
2
R
sin
A
,
b
=
2
R
sin
B
,
c
=
2
R
sin
C
So,
a
cos
A
+
b
cos
B
+
c
cos
C
a
+
b
+
c
=
R
(
sin
2
A
+
sin
2
B
+
sin
2
C
a
+
b
+
c
)
using
sin
2
A
+
sin
2
B
+
sin
2
C
=
4
sin
A
sin
B
sin
C
so, we get
=
4
R
(
sin
A
+
sin
B
+
sin
C
a
+
b
+
c
)
=
a
b
c
2
R
2
(
2
S
)
=
4
R
△
4
R
2
S
so we get
△
R
S
=
r
R
∴
a
cos
A
+
b
cos
B
+
c
cos
C
a
+
b
+
c
=
r
R
Hence, proved.
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