Proof of the Circle Theorems

Question 10

$B\,$ 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.

[4]

Proof of the Circle Theorems

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Question 10

$B\,$ 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.

[4]

Proof of the Circle Theorems

Question 10

Proof of the Circle Theorems Questions

Proof of the Circle Theorems

Question 10

Proof of the Circle Theorems Questions