Euclid: The Game Level 10 — Constructing Geometry via Quadratics and Intersectio

This example demonstrates how Level 10 of “Euclid: The Game” can be solved by constructing a planar geometry configuration using intersections between line segments and quadratic functions (parabolas). The key math ideas include quadratic function behavior, intersection of geometric entities (segments with curves/objects), and relationships that can be expressed through ratios and subtraction-type comparisons. Construction-wise, the GeoGebra workflow is driven by the commands Segment and Intersect: segments are created among key points (A, B, C, D, E, F, G), while f and g represent the functional objects whose graphs/associated geometry are used to find required intersection points via Intersect. The resulting intersection points serve as anchors to realize the target figure for the game. Suitable for secondary school learners and enrichment activities that connect algebra (quadratics) with geometric constructions.