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JEE Advanced Model Paper 1 with solutions for online practice
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© examsnet.com
Question : 51
Total: 60
If (1,2) is the centroid of an equilateral triangle and (-2,-2) is one of thevertices, then
inradius of triangle is
5
2
area of triangle is
225
4
equation of side opposite to vertex (-2, -2) is 6x + 8y = 47
area of the triangle is
225
4
√
3
Validate
Solution:
sin 30° =
I
D
√
9
+
√
16
⇒ ID (in radius) =
5
2
Also, AG =
√
9
+
16
= 5 ∴ BD (length of altitude) = 5 +
5
2
=
15
2
∴ area (ΔABC) =
h
2
√
3
=
225
4
√
3
Let co-ordinates of E (x,y)
So , 1 =
2
(
x
)
+
1
(
−
2
)
3
⇒ x =
5
2
Also , 2 =
2
(
y
)
+
(
−
2
)
3
⇒ y = 4
So , E
(
5
2
,
4
)
⇒
m
a
C
=
1
m
A
E
=
−
3
4
⇒ E
(
5
2
,
4
)
⇒
m
B
C
=
1
m
A
E
=
−
3
4
⇒ Equation of BC is (y - 4) =
(
−
3
4
)
(
x
−
5
2
)
⇒ 6x + 8y = 47
© examsnet.com
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