Two circles are orthogonal if they intersect at right angles, meaning their tangents at the points of intersection are perpendicular. The condition is 2g1g2 + 2f1f2 = c1 + c2 (for circles in general form). Equivalently, $d^2$ = $r1^2$ + $r2^2$, where d is the distance between centres. Each circle passes through the point where the other circle's tangent from the centre touches.