ajith wrote:rajs.kumar wrote:
Also for a circumcircle diameter d = height of the equilateral triangle.
I disagree with you here. Is it not 2/3 of the height?
Yes I am wrong and you are correct mate. I have to be more careful when posting, it is my mistake.
If we assume the side of the triangle to be b and height to be h they are related in this way
sin 60 = h/b => h = b x sqrt(3) / 2 --- (1)
area of triangle = 9 => b x h = 18 --- (2)
(1) in (2) => b^2 = 36/sqrt(3) --- (3)
the radius of the circumcircle r is related to the side b of the triangle in the following manner.
r/b/2 = sec 60 => r = b/sqrt(3) ---- (4)
using (4) So area of the circumcircle is PI x r^2 = PI x b^2/3 --- (5)
(3) in (5) => area = PI x 12/sqrt(3)
which is the same as what ajith got.
If you can remember the formula directly you will get the same result. The formula for area of the circucircle of equilateral triangle is 1/3 x PI x b^2 where b is the length of the side.
The formula gives the same value, area = PI x 12/sqrt(3)
