An Elliptic Identity
Let E be a point on an ellipse, O its center, F and G its two foci, and P the point on the tangent line to E such that OP is perpendicular to the tangent line. Then the identity is . Drag the point E to see that the identity holds for ellipses of different shapes and sizes.
"Problems and Solutions," The American Mathematical Monthly, 85(10), 1978 pp. 29–32, problem B-4.