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CAT Exam Model Paper 2 with solutions for free online practice
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© examsnet.com
Question : 72
Total: 100
In an equilateral triangle ABC, AO, BO and CO are the angle bisectors meet at the incentre ‘O’. D, E and F are the mid-points of AO, BO and CO respectively. A circle with centre ‘O’ passes through D, E and F. Area of the circle is 3π cm
2
. What is the perimeter of triangles (△) ABC?
12
√
3
cm
18 cm
6
√
3
cm
None of these
Validate
Solution:
(d)πr
2
= 3 π⇒ r = 3 cm
∴ DE = 2r
2
− 2r
2
cos120°
DE = 3r
2
(
∵
√
3
= r)
But AB = 2DE (By similarly of triangles)
∴ AB
=
2
(
3
r
2
)
=
6
×
(
√
3
)
2
=
18
cm
(∴D and E are the mid-points of OA and OB)
∴ Perimeter of triangle ABC = 3 × 18 = 54 cm
© examsnet.com
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