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Most people only ever learn the classic methods for finding the centre of a circle — using a square and a straightedge, dropping perpendiculars from two chords, or eyeballing a bisector. They work, but they’re not the whole story.
Below are several unique, highly accurate geometric techniques you’ve probably never tried before. Each one is based on pure construction geometry, requires nothing more than a compass and a straightedge, and reveals the centre or radius of a circle in surprisingly elegant ways.
Explore the interactive apps below to see these methods in action and learn how they outperform traditional sagitta and chord‑based measurements.







This page constitutes the original publication of Langley’s Lens Principle, and the original circle measuring techniques found on this page (May 6, 2026)