Ellipse and Median Value Demo

Create a geometry diagram demonstrating ellipse properties and a median-value style idea. Start with an ellipse and pick two points on it, then connect them to form a reference segment. Add annotation text along with input fields for two parameters. Using the entered values, construct a third point related to the chosen first point and draw a segment from the first point to this third point, then define a length/direction measure from that segment. Next, form an intersection determined by the ellipse and an additional line/constraint to obtain a key point, connect it with the ellipse points to form a triangle-like polygon, and mark the angle at the middle vertex between the two connecting segments. Include extra message text that can react to whether the measured length becomes zero and whether the inputs satisfy simple repetition/digit conditions.