# Perpendicular Circles

Geometry Level 3

Three different circles are all touching each other but not overlapping.

• One circle has center $$O$$ and radius 4,
• and another circle has center $$A$$ and radius 2,
• and another circle has center $$P$$ and radius $$r$$

Given that $$OA$$ is perpendicular to $$AP$$, find $$r$$.

×