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. Here's an interesting problem: Find \(\angle ABD,\) in the figure below.
Here's the solution. Additional practice problems can be found here. Here's another 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.