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Byju's Answer
Standard X
Mathematics
Sine Rule
If R is the...
Question
If
R
is the radius of the circumcircle of the
Δ
A
B
C
and
Δ
is its area, then
A
R
=
a
+
b
+
c
Δ
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B
R
=
a
+
b
+
c
4
Δ
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C
R
=
a
b
c
4
Δ
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D
R
=
a
b
c
Δ
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Solution
The correct option is
D
R
=
a
b
c
4
Δ
sin
A
a
=
1
2
R
⇒
R
=
a
2
sin
A
=
a
2.
2
△
b
c
=
a
b
c
4
△
.
Hence, the answer is
a
b
c
4
△
.
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Similar questions
Q.
Prove that:
For any
△
A
B
C
,
a
cos
B
cos
C
+
b
cos
C
cos
A
+
c
cos
A
cos
B
=
Δ
R
where
R
=
a
b
c
4
Δ
.
Q.
If R is the radius of circumcircle of
Δ
ABC, then
R
=
a
b
c
4
S
Q.
Relation between circumradius, side lengths and area of the triangle can be given by
R
=
a
b
c
4
Δ
where a, b, c represent the sides and
Δ
represents the area
Q.
In
Δ
A
B
C
the sides opposite to angles
A
,
B
,
C
are denoted by
a
,
b
,
c
respectively.
Let
a
2
+
b
2
=
c
2
. If
R
and
r
are its circumradius and inradius respectively then
R
+
r
is equal to?
Q.
A circle of radius r is inscribed in a triangle of area
′
Δ
′
. If the semi-perimeter of the triangle is s, then the correct relation is
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