Circle Theorem Calculator

Use the quick-check workspace to identify the theorem that matches your diagram, then compare the formula, visual relationship, and result with your own working. The page is designed as a reference companion for the tangent, chord, arc, and triangle tools, so you can verify the reasoning before copying a final value.

For the full explanations and worked context, open the detailed circle theorems guide, including the definitions, diagrams, formulas, and quick checks. 

Circle Theorems: Interactive Formula Guide

Choose a theorem, read the relationship in plain language, and click to check a worked example. This is designed for quick revision before solving a geometry question.

Choose a theoremAngle at the centreInscribed angle theoremAngle in a semicircleAngles in the same segmentCyclic quadrilateralTangent and radiusAlternate segmentPerpendicular from centre to chordIntersecting chordsTangent-secant

Click-to-check workspace

Quick reference

Centre angle: centre angle = 2 × circumference angle.

Inscribed angle theorem: an angle at the circumference is half the angle at the centre standing on the same arc.

Semicircle: an angle standing on a diameter is 90°.

Same segment: angles standing on the same chord are equal.

Cyclic quadrilateral: opposite angles add to 180°.

Tangent-radius: the radius at the contact point is perpendicular to the tangent.

Alternate segment: the tangent-chord angle equals the angle in the opposite segment.

Chord: a perpendicular from the centre bisects a chord.

Intersecting chords: segment product on one chord equals segment product on the other.

Tangent-secant: tangent² = external secant × whole secant.