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This topic applies circle geometry to coordinate problems — the perpendicular from the centre to a chord, a tangent meeting a radius at 90°, and chord properties — to find tangents, lengths and unknown points. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
A tangent meets the radius at right angles, so find the radius gradient and take its negative reciprocal. The perpendicular bisector of a chord passes through the centre. For intersections, substitute the line into the circle and use the discriminant to count solutions.
Before you start
It assumes you can handle circle equations and perpendicular gradients. This is the foundation for geometric problem solving.
What you learn
That single fact gives you the tangent's gradient, and so its equation. Given any two of the three, Pythagoras gives you the third. Does a line cut a circle, touch it, or miss it entirely? The course works through tangent perpendicular to radius, the perpendicular from the centre bisects a chord, line and circle: the discriminant, the length of a tangent and problem solving. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Circles — Tangents & Chords belongs to Coordinate Geometry and is met in the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Related topics students usually take next include Distance & Midpoint, Parametric Equations, Straight Lines and Circles — Equation & Properties. Endless extra practice on this strand is available on the Coordinate Geometry revision engine, which generates a fresh question each time.
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