3
You visited us
3
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Construction of Incircle
In a ABC with...
Question
In a
△
A
B
C
with usual notation, if
∠
A
=
∠
B
=
1
2
(
sin
−
1
(
√
6
+
1
2
√
3
)
+
sin
−
1
(
1
√
3
)
)
and
c
=
6
⋅
3
1
/
4
,
then the area of
△
A
B
C
in square units, is
Open in App
Solution
Let
sin
θ
=
√
6
+
1
2
√
3
2
A
=
2
B
=
sin
−
1
(
√
6
+
1
2
√
3
)
+
sin
−
1
(
1
√
3
)
∴
2
A
=
2
B
=
tan
−
1
(
1
+
√
6
√
3
−
√
2
)
+
tan
−
1
(
1
√
2
)
=
cot
−
1
(
√
3
−
√
2
1
+
√
3
⋅
√
2
)
+
tan
−
1
1
√
2
=
π
2
−
[
tan
−
1
√
3
−
tan
−
1
√
2
]
+
tan
−
1
1
√
2
=
π
2
−
tan
−
1
√
3
+
tan
−
1
√
2
+
cot
−
1
√
2
=
π
−
tan
−
1
√
3
=
2
π
3
⇒
2
A
=
2
B
=
2
π
3
⇒
A
=
B
=
π
3
⇒
∠
C
=
π
3
∴
△
A
B
C
is equilateral.
Hence, area
=
√
3
4
×
c
2
=
√
3
4
×
36
×
√
3
=
27
sq. units
Suggest Corrections
1
Similar questions
Q.
With usual notation, if in a triangle
A
B
C
,
a
+
3
=
b
+
2
=
11
and
cos
C
=
2
3
,
then
Q.
With usual notation, if in a triangle
A
B
C
,
cos
A
cos
B
+
sin
A
sin
B
sin
C
=
1
, then
a
:
b
:
c
=
x
:
x
:
y
. The value of
2
√
2
y
is
Q.
In a triangle ABC,
c
o
s
A
a
=
c
o
s
B
b
=
c
o
s
C
c
If a=
1
√
6
then the area of the triangle (in square unit) is
Q.
With the usual notation, in
△
A
B
C
, if
∠
A
+
∠
B
=
120
∘
,
a
=
√
3
+
1
and
b
=
√
3
−
1
, then the ratio
∠
A
:
∠
B
, is :
Q.
In a triangle
A
B
C
, with usual notations, if
∣
∣ ∣
∣
1
a
b
1
c
a
1
b
c
∣
∣ ∣
∣
=
0
, then
sin
2
A
+
24
sin
2
B
+
36
sin
2
C
is equal to
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Construction of Incircle
MATHEMATICS
Watch in App
Explore more
Construction of Incircle
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app