Hussain15 wrote:
Thanks to both of you for giving your valuable feedback.
After spending 15 minutes, now I got the issue. Actually both of you mentioned \(3\sqrt{3}\) as the area of the smaller triangle, & thats correct, but when you have subtracted \(\sqrt{3}\) from \(3\sqrt{3}\), you didnt mention that this \(3\sqrt{3}\) is not the area of smaller triangle, rather its the height of the larger triangle. Then you have subtracted the height of smaller triangle from the height of larger triangle, ultimately giving us the radius of the circle. Now its making sense for me. :)
Thanks again guys!!,
Just wanted to contribute how I solved the problem...I used the centroid concept
The side of the equilateral triangle can be calculated to 6 units.
s=6, therefore height =\({(sqrt(3)/2)s}\) = \({3sqrt(3)}\)
When an equilateral triangle is inscribed in a circle, the centroid(point where the three medians meet) coincides with the centre of the circle. So all we need to calculate the radius is to calculate the length from the centroid to one of the vertices of the triangle.
The
length of the segment from the centroid to the vertex(i.e. radius of the circle) is (2/3)* height of the triangle
Therefore, radius = \({(2/3)3sqrt(3)}\) = \({2sqrt(3)}\)
Thus area of the circle = \(12pi\)
Hope it helps,
meshtrap
Does the formula highlighted and bold works for all types of triangle or only for an equilateral triangle?