Tangent Function and Incircle Dynamic Exploration Example

①This example demonstrates how to construct a dynamic geometric figure in GeoGebra that includes a tangent function graph, an incircle, and interactive points, allowing real-time parameter adjustments via sliders and input boxes. ②Core mathematical concepts include the tangent function, incircle (inscribed circle), trigonometry, geometric construction, and the interplay between functions and geometry. ③Construction highlights: from the summary, commands such as Point, Vector, Textfield, Segment, Line, Intersect, OrthogonalLine, and Ray are used to create base objects; input boxes (inputBox1, inputBox2) and a button (button1) enable interactive parameter control; Focus and Circle commands help construct the incircle; multiple points, lines, circles, and text labels (text3, text4) are included for annotation. ④Suitable for high school or early college students to explore trigonometric graphs, geometric constructions, and dynamic mathematics, and also useful for teachers creating interactive lesson materials.