Radius and tangent theorem

Students will see a proof of the following theorem: If there is a circle with radius \(OA,\) and a tangent going through \(A,\) then the radius and tangent are perpendicular. Then students will learn how to use this theorem to solve some geometry problems. You can see examples here, here, and here. Additional practice problems can be found here. Here's an especially interesting problem: There is a circle with center \(X\) and another circle with center \(Y.\) Their single point of contact is point \(K.\) Prove that \(X,\) \(K,\) and \(Y\) are collinear. Here's the solution.