Tracking All Possible Outcomes: Logical Exhaustion with Geometry

This example demonstrates a practice on systematically tracking and classifying all possible outcomes under given conditions. It emphasizes logical exhaustion (listing cases and ruling out invalid ones) to reach the correct conclusion and corresponding geometric configuration. The mathematical themes include logic-based casework, relationships tied to trigonometric function ideas, similarity transformations (corresponding angles/ratios), and geometry elements such as the orthocenter and tangent-function context. In the GeoGebra workflow, the construction is centered around a primary figure (noted as the object pic1), where key geometric objects used for case analysis—angles, constructed correspondences from similarity transformations, and angle conditions connected to tangent/trigonometric relationships—are built and checked interactively. Suitable for advanced secondary school students and enrichment/olympiad preparation, especially for lessons combining function reasoning with geometric casework.