Consider a point outside of a circle. Suppose two line segments share this endpoint and have their other endpoints on the circle so that one of them passes through the circle and the other does not. If the area of the square formed using the length of the segment that does not pass through the circle is 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, then the line segment that does not pass through the circle is tangent to it.
