The diameter? This is a segment that connects two points of the circle and passes through its center. Also the diameter is called the length of this segment.
Let's consider some ways of calculation of diameter of a circle depending on the initial data.
Diameter (D) in size is equal to two radii (R):
D = 2 * R
If the circumference (L) is known, then:
L = 2 * Pi * R
D = L / Pi
If the area of the circle (S) is known, then:
S = Pi * R ^ 2
D = 2 * v (S / Pi)
In the Cartesian coordinate system:
General equation of a circle with center at the origin:
X ^ 2 + y ^ 2 = R ^ 2, hence
D = 2 * v (x ^ 2 + y ^ 2)
If the coordinates of both ends of the diameter (x1, y1) and (x2, y2) are known:
D = v ((x1-x2) ^ 2 + (y1-y2) ^ 2)
In the case of a circle circumscribed about a triangle:
A / sin (alpha) = b / sin (beta) = c / sin (gamma) = 2R = D,
Where a, b, c? Sides of a triangle, and alpha, beta and gamma? The angles opposite to them.
Formulas for the radii of inscribed (r) and circumscribed (R) circles of a triangle:
R = a * b * c / (4 * S)
R = 2 * S / (a + b + c),
Where a, b, c? Sides of a triangle, S - its area.