Angle Bisectors and Incenter: Incircle Discovery

①This GeoGebra example demonstrates the incenter and incircle of a triangle through an investigative discovery approach. It shows that the three angle bisectors of a triangle are concurrent at a single point (the incenter), and the circle centered at this point tangent to all three sides is the incircle. ②Core mathematical concepts include angle bisectors, concurrency, incenter, incircle, distance from a point to a line, and the relationship between triangle area and semiperimeter. ③Construction highlights: using GeoGebra commands such as Segment, Polygon, Angle, Rotate, Line, Intersect, OrthogonalLine, and Circle to construct the triangle, its angle bisectors, the incenter, and the incircle; additional tools like PointIn and Slope support exploration. ④This is ideal for middle school or high school geometry classes, enabling students to discover the incenter theorem and the uniqueness of the incircle through guided questions, suitable for classroom activities or self-study.