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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 12
Total: 100
Two tangents are drawn from the point
P
(
−
1
,
1
)
to the circle
x
2
+
y
2
−
2
x
−
6
y
+
6
=
0
. If these tangents touch the circle at points
A
and
B
, and if
D
is a point on the circle such that length of the segments
A
B
and
A
D
are equal, then the area of the
△
A
B
D
is equal to
[2021, 27 July Shift-I]
2
(
3
√
2
+
2
)
4
3
(
√
2
−
1
)
Validate
Solution:
C
:
x
2
+
y
2
−
2
x
−
6
y
+
6
=
0
(
x
−
1
)
2
+
(
y
−
3
)
2
=
2
2
A
P
=
Length of tangent
=
√
S
1
⇒
A
P
2
=
(
−
1
−
1
)
2
+
(
1
−
3
)
2
−
4
⇒
A
P
2
=
4
+
4
−
4
∴
A
P
=
2
tan
θ
=
A
O
A
P
=
2
2
=
1
(
∴
θ
=
45
∘
)
In
△
A
C
O
,
A
C
A
O
=
cos
θ
∴
A
C
=
2
×
1
√
2
=
√
2
∴
△
O
A
C
≅
△
O
A
M
∆
O
A
C
≅
D
O
B
C
∆
O
B
C
≅
△
O
D
M
∴
Area of
△
A
B
D
=
4
Area of
△
A
C
O
=
4
×
1
2
(
A
O
×
A
C
×
sin
θ
)
=
2
×
2
×
√
2
×
1
√
2
=
4
© examsnet.com
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