Touching Circles – Radii, Centres, Equations & Intersections

Circle 1 radius:
Circle 2 radius:

Lock Circle 1 position
Force external tangency

Values

Intersection Points

Circle Equations

Algebraic Relationships

d = √((x₂−x₁)² + (y₂−y₁)²)

External tangency: d = r₁ + r₂

Internal tangency: d = |r₁ − r₂|

a = (r₁² − r₂² + d²) / (2d)

h = √(r₁² − a²)

P = C₁ + (a/d)(C₂ − C₁)

I₁,₂ = P ± (h/d)(−(y₂−y₁), x₂−x₁)