Proof of the Circle Theorems

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Hard

$B\,$ and $C\,$ are points on the circumference of a circle, centre $O$ . $DCE\,$ is a tangent to the circle.

A geometric diagram showing a circle with center O. A horizontal line DCE is tangent to the circle at point C. Points A and B are on the circumference. Chords AC and BC are drawn. Angle BAC is the inscribed angle subtending arc BC. Angle BCE is the angle between the tangent line CE and the chord BC.

Prove that angle $BCE\,$ and angle $BAC\,$ are equal.

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Proof of the Circle Theorems Questions

Practise AQA GCSE Maths Proof of the Circle Theorems with exam-style questions for Foundation and Higher tier. 20 questions, matched to the AQA GCSE Maths (8300) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.