Ptolemy’s Theorem with a Cyclic Quadrilateral

This example visualizes Ptolemy’s Theorem by constructing a cyclic quadrilateral from four points on the same circle and comparing the involved segment-length relationships. It centers on: cyclic quadrilaterals (four concyclic points) and Ptolemy’s Theorem, which connects the products of opposite sides to the product of the diagonals. The construction is carried out with GeoGebra commands such as Circle (to define the circumcircle and points), Polygon (to form the quadrilateral), and Segment (to draw and measure the sides/diagonals). Labeled objects (e.g., text labels) present the theorem expression and the key quantities. Suitable for secondary-school geometry and early university geometry modules, as well as self-study for theorem exploration and verification through measurement.