Envelope (Plane Geometry)/Examples

Examples of Envelopes in context of Plane Geometry

Circles with Centers on Circle

Let $\CC$ be a circle with radius $r$ with center at $O$.

Let $\SS$ be the set of circles with radius $a$ whose centers all lie on the circumference of $\CC$.

Then the envelope of $\SS$ consists of:

a circle with radius $r + a$ with center at $O$

a circle with radius $\size {r - a}$ with center at $O$.