Equal-Angle Property of Tangent to an Ellipse at a Focus

This GeoGebra example demonstrates a classic property of an ellipse: if A and B are the two foci and D is any point on the ellipse, then the angle between the tangent at D and line AD equals the angle between that tangent and line BD. In other words, the tangent bisects the external angle formed by the focal radii. The core mathematical concepts include the definition of an ellipse, foci, tangents, angle equality, and the reflective property. The construction uses GeoGebra commands: Ellipse to create the ellipse, Point to place a movable point D on it, Segment to draw focal radii AD and BD, Tangent to construct the tangent line at D, Angle to measure the two angles α and β, and Name to label objects. This is suitable for high school or undergraduate analytic geometry courses, serving as a dynamic visual proof of the optical property of ellipses, and can be used for inquiry-based learning or classroom demonstrations.