the main formula of the circle's equation is (x-a)²+ (y-b)² = R² where C(a, b) is the center of the circle R is the radius
if a point A(x', y') passes through the circle, so the equation of the circle can be written as (x'-a)²+ (y'-b)² = R², and that is a main formula.
<span>Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2), so we have exactly three equation: </span> (0-x)² + (0-y)² = R², circle O passes through A x²+y²= R² (-3 -x)² + (0-y)² = R², circle O passes through B (-3 -x)² + (y)² = R² (1-x)² + (2-y)² = R², circle O passes through A (1-x)² + (2-y)² = R²
and we know that R= OA = OC= OB, OA=R= sqrt( (0-x)² + (0-y)² ) = OB = sqrt((-3 -x)² + (0-y)²), this implies
x²+y² = (-3 -x)² + (0-y)² , it implies x² = 9+ x² + 6x , and then -9/6=x, x= -3/2 and when OA = OC x²+y² =(1-x)² + (2-y)² so, x²+y² =1+x²-2x +4+y²-4y, therefore -5= -2x -4y -5= -2x -4y, when x = -3 /2 we obtain y = 2
<span>Based on the problems I have recently done on FLVs with this though, is that if you connect the center of the arcs to the top intersection point, if the angle degrees, and opposite arcs are the same then it is an equilateral triangle.</span>