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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 34
Total: 100
Let the orthocentre and centroid of a triangle be
A
(
−
3
,
5
)
and
B
(
3
,
3
)
respectively. If
C
is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :
[2018]
2
√
10
3
√
5
2
3
√
5
2
√
10
Validate
Solution:
Since Orthocentre of the triangle is
A
(
−
3
,
5
)
and centriod of the triangle is
B
(
3
,
3
)
,
then
A
B
=
√
40
=
2
√
10
Centroid divides orthocentre and circumcentre of the triangle in ratio 2: 1
∴
A
B
:
B
C
=
2
:
1
N
o
w
,
A
B
=
2
3
A
C
⇒
A
C
=
3
2
A
B
=
3
2
(
2
√
10
)
⇒
A
C
=
3
√
10
∴
Radius of circle with
A
C
as diametre
=
A
C
2
=
3
2
√
10
=
3
√
5
2
© examsnet.com
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