If the four vertices of an equilateral pyramid are on a sphere of radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the equilateral pyramid is The answer to this question is that the bottom is an equilateral triangle and the radius of the ball is 1 The side length of the bottom surface is √ 3, The bottom area is 3 √ 3 / 4, ∴V=1／3×3√3／4×1=√3／4． I want to know why the side length of the bottom is root three. Is there any formula

If the four vertices of an equilateral pyramid are on a sphere of radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the equilateral pyramid is The answer to this question is that the bottom is an equilateral triangle and the radius of the ball is 1 The side length of the bottom surface is √ 3, The bottom area is 3 √ 3 / 4, ∴V=1／3×3√3／4×1=√3／4． I want to know why the side length of the bottom is root three. Is there any formula

∵ the three vertices of the bottom surface are on the big circle of the ball, that is: the diameter of the circumscribed circle of the equilateral triangle on the bottom surface is the diameter of the ball, where OA = ob = OC = r = 1 ∠ BOD = ∠ cod = 60 ° BD = CD = ocsin60 ° = 1 * √ 3 / 2 = √ 3 / 2BC = 2bd = √ 3