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This topic covers the circle theorems — angles in a semicircle, at the centre and circumference, in the same segment, cyclic quadrilaterals and tangents — used with reasons in proofs. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Learn the theorems and name the one you use each time. The angle at the centre is twice the angle at the circumference; angles in the same segment are equal; the angle in a semicircle is 90; opposite angles in a cyclic quadrilateral total 180; and a tangent meets a radius at 90.
Before you start
This builds directly on angle facts and circle vocabulary. Getting it right here pays off in geometric proof. It is Higher tier material at GCSE and iGCSE.
What you learn
A handful of theorems link the angles and lines inside a circle. In the exam you rarely just state them — you use them to find missing angles, and you must give the reason each time. When the same arc AB is ‘seen’ from the centre and from the circumference, the angle at the centre is twice the angle at the circumference. Angles standing on the same arc, from the same segment, are equal. The course works through angle at the centre, and the semicircle, same segment, and cyclic quadrilaterals and tangent theorems. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our GCSE maths courses, Circle Theorems belongs to Geometry and is met in Higher tier. It runs to 3 concepts, each followed by a check, with 2 worked examples along the way. Nearby topics in the same strand are Circles, Loci & Construction, Pythagoras' Theorem, Sine & Cosine Rule and Transformations. You can drill this strand further on the Geometry revision engine, with your accuracy saved to your skill tree.
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