Exercise 7 Solution: Constructing intersection geometry and linking with inequal

This example demonstrates how to build a solution by constructing key points and geometric quantities from basic operations, then using the resulting constraints in an equation/inequality-style reasoning (including geometric-mean type quantities). The main mathematical ideas include: intersection of lines to determine critical points, angle bisectors to encode equal-angle conditions, orthogonal (perpendicular) constructions to impose right-angle constraints, and area measurements of a polygonal region to connect geometry with algebraic expressions. Construction highlights (from the provided GeoGebra summary): Polygon to form the relevant polygonal region and obtain its Area; Line to create the guiding lines (with points and named elements such as P, Q, R and variables like p, q, r, as reflected in the object list); Intersect to compute intersection points that drive the configuration; OrthogonalLine to construct perpendicular lines linked to helper objects like OrtoC and auxiliary distances/markers (e.g., d, e); and LineBisector to create angle-bisector relationships (corresponding to quantities b, c). The configuration also includes CircunC for a circular constraint/auxiliary construction, tying the geometric framework to the named parameters a, b, c. Suitable for secondary-level geometry construction practice, exam/contest preparation, and classroom demos using GeoGebra.