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AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 28
Total: 160
Let a triangle ABC be inscribed in a circle of radius 2 units. If the 3 bisectors of the angles A. B and C are extended to cut the circle at
A
1
,
B
1
and
C
1
respectively, then the value of
[
A
A
1
c
o
s
A
2
+
B
B
1
c
o
s
B
2
+
C
C
1
c
o
s
C
2
s
i
n
A
+
s
i
n
B
+
s
i
n
C
]
2
=
4
16
25
1
Validate
Solution:
The triangle
A
B
C
is equilateral
Therefore,
A
=
B
=
C
=
60
∘
Substitute the value in the given expression.
[
A
A
1
cos
A
2
+
B
B
1
cos
B
2
+
C
C
1
cos
C
2
sin
A
+
sin
B
+
sin
C
]
2
=
{
4
cos
60
∘
2
+
4
cos
60
∘
2
+
4
cos
60
∘
2
sin
60
∘
+
sin
60
∘
+
sin
60
∘
}
2
=
[
4
×
3
√
3
2
3
√
3
2
]
2
=
16
© examsnet.com
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