Two circles are orthogonal when they intersect at right angles — their tangents at the intersection points 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. A key property: if two circles are orthogonal, the tangent from the centre of one circle to the other has length equal to its own radius. Orthogonality problems in JEE often involve finding a circle orthogonal to two given circles, which gives two linear conditions on the three unknowns g, f, c, requiring one additional condition.