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Circle Theorem 4: Opposite Angles in a Cyclic Quadrilateral Sum to ? (+ converse)
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Circle Theorems are probably the only bit of GCSE Mathematics that tries to introduce the importance of proof, and has the potential to be the most engaging, if we ignore the significance of exams. However, what’s not covered is whether a theorem has a converse or not, I.e. whether the reverse statement of a proof is true or if A means B, does B also mean A type of vibe. These converses have quite a large significance, when it comes to Olympiad contest problems, as these theorems give rise to a rich source of problem solving. Geometry as a whole is practically amiss in the school curriculum, particularly at A-Level, where co-ordinate methods or calculus are preferred, but they don’t possess the same class of geometric methods and proofs.