Heron's Formula Proof Without Words: Geometric Construction with Incircle

This GeoGebra applet demonstrates a visual proof of Heron's formula for calculating triangle area without words. The core mathematical concepts include Heron's formula S=√[p(p-a)(p-b)(p-c)], properties of triangle incircles, angle bisector theorem, and similar triangles. Construction highlights: Using Ray and AngularBisector to locate the incenter, Segment to draw triangle ABC, Circle to create the incircle, Polygon to construct auxiliary figures, Distance and Angle to measure side lengths and angles. Suitable for middle and high school mathematics teachers demonstrating triangle area formulas, or as teaching material for geometric proof instruction to help students understand the geometric principles behind the formula.