Two circles are said to be orthogonal if the tangent at their point of intersection are at right angles.

Let the two circles be

x^{2} + y^{2} + 2g_{1}x + 2f_{1}y + c_{1} = 0

x^{2} + y^{2} + 2g_{2}x + 2f_{2}y + c_{2} = 0

The required **condition for orthogonality** is

**2g _{1}g_{2} + 2f_{1}f_{2} = c_{1} + c_{2}**