Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a distance d apart are orthogonal if r_1^2 + r_2^2 = d^2. Two circles with Cartesian equations x^2 + y^2 + 2g x + 2f y + c | = | 0 x^2 + y^2 + 2g' x + 2f' y + c' | = | 0 are orthogonal if 2g g' + 2f f' = c + c'.

circle | midcircle | Monge's problem | radical center | radical circle