Orthogonal Circles

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

Let the two circles be

x² + y² + 2g₁x + 2f₁y + c₁ = 0

x² + y² + 2g₂x + 2f₂y + c₂ = 0

The required condition for orthogonality is

2g₁g₂ + 2f₁f₂ = c₁ + c₂