Subject
Geometry
Geometry is at the heart of our teaching philosophy. Spatial reasoning develops the visual intuition that makes every branch of mathematics more accessible. We teach geometry deeply — not as a collection of formulas, but as a system of logical relationships.
The Geometry pathway
Ages 13–16 · Years 9–11
Circle theorems and classical constructions
Students explore the full breadth of classical Euclidean geometry — circle theorems, cyclic quadrilaterals, angle-in-semicircle, and the elegant constructions that have appeared in competitions for centuries.
What we cover
- Circle theorems and tangents
- Cyclic quadrilaterals
- Loci and constructions
- Trigonometry: sine, cosine, tangent rules
- Coordinate geometry and conic sections
Competitions & exams we prepare for in United Kingdom
- Intermediate Mathematical Challenge (geometry)
- Cayley / Hamilton / Maclaurin Olympiads
- Grey / Pink Kangaroo
Topics we explore
Axioms and Postulates of EuclidView on ProblemsMinimum and Maximum Problems in GeometryMinimum and Maximum Problems in GeometryView on ProblemsFixed Point of a SimilarityInteractive geometry demo: scale, rotate, and drag a shape to see the invariant point appear, then try the guess-the-point challenge mode.View on ProblemsMathematics in ChessAn overview of chessboard problems about parity, move graphs, extremal placements, exact-opponent attacks, and Knight's Tour, with focused guides below.View on ProblemsOther Chessboard ProblemsA pair of chessboard construction problems driven by row-column counts and Hamiltonian-style reasoning on custom move graphs.View on ProblemsChallenging Triangle CongruenceMost students are already familiar with the three standard triangle congruence rules taught in school: SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle). These form the foundation of geometry and are commonly seen in classroom exercises and exams, including the GCSE Mathematics syllabus.But what happens when we encounter problems that don’t follow these standard patterns directly? Can we still prove triangle congruence using medians, altitudes, angle bisectors, or partial side information?In this section, we explore a selection of challenging triangle congruence problems that require deeper reasoning and clever constructions. These problems go beyond the textbook basics and are perfect for students preparing for Olympiad-style questions, GCSE extensions, or anyone wanting to sharpen their proof skills.View on ProblemsCircumcircle of a TrianglePractice problems on circumcircles of triangles: centers, angles, chords, and construction. Ideal for Olympiad geometry and advanced learners.View on ProblemsInscribed QuadrilateralLearn the theory and solve challenging problems about inscribed quadrilaterals. Perfect for math Olympiad prep, this page covers trapezoids, kites, and key geometric proofs.View on ProblemsPythagoras' theoremThese problems use the Pythagoras theorem and its consequences (perpendicularity criteria, projections, and equal‑tangent loci) to prove algebraic relations and describe geometric sets.View on ProblemsTangentExplore key theorems about tangents to circles and solve problems involving radii, angles, and geometric constructions with tangents.View on Problems
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