Theorem: A radius and a tangent that intersect at the point of tangency are perpendicular.

Given circle A with radius AC and tangent CD, prove that AC and CD are perpendicular.

Try proving this theorem using an indirect proof. Assume that AC and CD are NOT perpendicular. This implies that there is another point on C, say C', such that AC' and CD are perpendicular. From this information, deduce logically until you reach a conclusion that either contradicts the given or is false.