# Oval Calculator

An oval is a closed curve in a plane that “faintly” resembles the contour of an egg. Usually an oval is considered as a round, convex shape without a vertex and with one axis of symmetry. This special oval is formed by two circles with radii R and r and distance a from their centers. A third circle is laid around both circles, which touches each of them at one point. The center of this is at the intersection of two lines through the touch points and the centers of the other two circles. The area formed by this is a flat projection of a spherical triangle, added to the two circles. This is repeated on the other side of both circles.

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Oval Calculator The radius of the larger circle (R)
The radius of the smaller circle (r)
Distance between centers (a)
The radius of the union of circles (ρ)
Square (S)

## Formulas

ρ = ( a² + R² – r² ) / [ 2 * ( R – r ) ]

S = 1/2 * { a(R-r) + π(r2+R2) – a3/(R-r) + [a2+(R-r)2] * (a2-3r2+2rR+R2) / [ 2 * ( R – r )2 ] * arctan[ (2a(R-r)) / (a2-(R-r)2) ] }

If a ≤ R – r: S = π * R2
(identical to a circle with radius R, there is no connecting circle)

If R = r: ρ=∞, S = π * R2 + 2 * a * R