Tangent to Ellipse Theorem: Rectangle and Rhombus from Focal Lines

This GeoGebra example demonstrates a geometric theorem about tangents to an ellipse: when a tangent is drawn at a point on the ellipse and lines are connected to the two foci, the resulting configuration reveals special rectangles and rhombi. The core mathematical concepts include the definition of an ellipse, tangent properties, foci, and the angle/edge relationships in quadrilaterals formed by tangent, normal, and focal segments. Construction steps: use the Ellipse command to create the ellipse, place a point on it with Point, draw the tangent using Tangent, find intersections with Intersect, connect foci and tangent point using Line, and finally apply the Prove command to verify the theorem (e.g., the tangent bisects the external angle between focal radii, or certain quadrilaterals are rectangles/rhombi). Suitable for high school and above for studying analytic geometry, conic tangent properties, or for dynamic verification of geometric theorems.