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 \(r\).

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