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sunil kumar mishra

· started a discussion

· 1 Months ago

This is regarding question circumcircle and incircle in the given question. (Question: 115415.0 )

in question circle is inscribed. but in your circle you have taken it as a circumcircle. so pls clear this issue, Thank u.

Question:
The area of an equilateral triangle inscribed in a circle is 9√3cm2. The area of the circle is:
Options:
A) 8√3cm2               
B) 13π cm2       
C) 12 π cm2
D) 36 π cm2
E) None of these
Solution:

Area of equilateral ∆ = \(\cfrac{\sqrt{3}}{4}\) (a)2

= 9√3


a=6

⇒ circum-radius of equilateral ∆ = \(\cfrac{a}{\sqrt{3}}\)  = \(\cfrac{6}{\sqrt{3}}\) = 2√3

So, area of circle = π × (2√3)2 = 12 π cm2

Knowledge Expert

· commented

· 1 Months ago

The area of an equilateral triangle inscribed in a circle is 9√3cm^2. The area of the circle is: Area of equilateral ∆ = √(3)/4 * (a)^2 = 9√3 a=6 ⇒ circum-radius of equilateral ∆ = a/√(3) = 6/√(3) = 2√3 So, area of circle = π × (2√3)^2 = 12 π cm^2
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