Prachikh wrote:

i tried doing the following:

since one side of the triangle is the diameter, the triangle becomes a right triangle inscribed in the circle. Hence is not equilateral and the statement becomes void. M i using the right logic?

Hi

I dont think its correct to say that the statement

becomes void. There is an equilateral triangle separately whose side is say 'x'. So its perimeter becomes '3x'.

Now there is another circle separately which happens to have the same diameter as the length of side of our equilateral triangle, i,e, 'x'.

So here we have to compare perimeter of an equilateral triangle with side x, and circumference of a circle with diameter x. It doesn't mean that our earlier triangle has to be inscribed in this circle.