Circle Tangent to a Circle and Passing Through a Fixed Point

Circle Tangent to a Circle and Passing Through a Fixed Point

If the required circle has centre $$p$$ and radius $$r$$, passes through fixed point $$a$$, and is externally tangent to a circle with centre $$o$$ and radius $$r$$:

$$PA=r,\quad OP=R+r$$

Usage

- Used to determine a circle satisfying a fixed-point condition and an external tangency condition.