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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Multiples of an Angle
The angles of...
Question
The angles of a right-angled triangle are in
A
.
P
.
The ratio of the inradius and the primeter is
A
(
2
−
√
3
)
:
2
√
3
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B
1
:
8
√
3
(
2
+
√
3
)
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C
(
2
+
√
3
)
:
4
√
3
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D
none of these
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Solution
The correct option is
A
(
2
−
√
3
)
:
2
√
3
(
α
−
β
)
+
α
+
(
α
+
β
)
=
180
0
and
α
+
β
=
90
0
∴
the angles are
30
0
,
60
0
,
90
0
∴
a
sin
30
0
+
b
sin
60
0
+
c
sin
90
0
=
2
R
⇒
a
=
R
,
b
=
√
3
R
,
c
=
2
R
r
=
Δ
s
=
1
2
.
R
.
√
3
R
1
2
(
R
+
√
3
R
+
2
R
)
=
√
3
R
3
+
√
3
and
2
s
=
R
+
√
3
R
+
2
R
=
(
3
+
√
3
)
R
∴
r
2
s
=
√
3
R
3
+
√
3
×
1
(
3
+
√
3
)
R
=
1
(
3
+
√
3
)
(
√
3
+
1
)
=
1
6
+
4
√
3
=
1
2
√
3
(
2
+
√
3
)
=
2
−
√
3
2
√
3
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