Euclid's Elements - Book III, Proposition 36

Author:
mtpberg
Topic:
Circle
Consider a point outside of a circle. Suppose two line segments share this as one endpoint and have other endpoints on the circle so that one of them is tangent to the circle and the other one passes through the circle. Then the area of the square formed using the tangent line segment’s length will be equal to the area of the rectangle formed using as side lengths the whole of the other line segment and the portion of that segment that lies outside of the circle.