Question

An equilateral triangle is inscribed in a circle. Each side of the triangle has length x. What is the area of the circle?
Please help

Answer 1

since the medians intersect 2/3 of the way from each vertex to the opposite side,

r = 2/3 (√3/2 x) = x/√3
so, the area is
a = πr^2 = π/3 x^2

Answer 2

half teh equilateral traingle is has agles 30 60 and 90 meanning taht its side lenghts will hav ratio 1 √3 to 2 so the heigh of teh equilateral triangle wud be √3x and since teh circummcentre separats teh perependicular bisextors 1 to 2 teh raidus of the circl wud be 2/3 of teh height of teh traingle which was √3x and if u multipl tehn u get radius is 2(√3x)/2 and if u didt kno teh area of circle is πr² mening if u subsitude radius in u get taht teh circl area is [2(√3x)/2]²π which if u caclate and simpify then u get the arrea is 4/3x²π. Cheez is so good