Proof that Perpendicular Bisectors of Segments Meet at One Point

This example demonstrates a classic geometric proof: the perpendicular bisector of a segment is the locus of points equidistant from the segment’s endpoints, and the perpendicular bisectors of two segments (constructed from triangle vertices) intersect at a single point where the relevant distances are equal. The key concepts include perpendicular bisector properties, equidistance (distance-equality) reasoning, and the role of triangle structure in defining an “equidistant center.” Construction in GeoGebra uses Segment to create the given points/segments (e.g., A, B, C and related segments), LineBisector to construct the perpendicular bisectors (e.g., s_c, s_b), and Intersect to compute their intersection point (e.g., O). The resulting configuration supports proving that the intersection point satisfies the equidistance conditions. Suitable for secondary school geometry instruction, teacher demonstrations, and students practicing formal proof and geometry constructions.