CAT Exam Model Paper 2 with solutions for free online practice

Question : 72 of 100

Marks: +1, -0

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

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