Interactive Demonstration of Trigonometry and Piecewise Functions

In one coordinate plane, create an interactive construction: start with two points and draw the segment between them, then add a label showing that segment’s length-related text. Provide three input fields to control parameters, and generate a third point as the intersection of a circle centered at the first point with a radius defined from those inputs. Connect this point to the corresponding endpoints to form the key segments, include a conditional message that switches between “Too short!”, “Too long!”, or “This value is correct!”, and form a polygon (triangle-like) using the original endpoints and the computed intersection point. Measure and display the angle defined by three of the points, and add another conditional text based on a length check so the annotations update with the parameters.