Perpendicular from an Outer Point: Circle–Line Intersection Construction

① This GeoGebra exercise demonstrates how to construct a perpendicular from an outer point to a given line/constructed element using a classic circle–intersection method. ② The key ideas are perpendicularity criteria, the equal-distance property of circles, and using intersections of geometric primitives to identify the required points and enforce the right-angle condition. ③ The construction follows the provided command summary: Line to create the necessary lines (objects such as a and c), Circle to draw auxiliary circles (center/points like A, B, C and parameters tied to objects b and d), and Intersect to compute the intersection points (e.g., D and other derived points). These intersection-derived points are then connected to obtain the final perpendicular configuration. ④ Suitable for middle to early high school geometry practice, classroom demonstrations on geometric construction, and students learning proof-by-construction techniques.