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More Lessons for GCSE Maths

Math Worksheets

Examples, solutions, and videos to help GCSE Maths students learn the circle theorems.

• Angle subtended at the centre of a circle is twice the angle at the circumference.

• The angle between a radius and a tangent is 90 degrees.

• The angle at the centre is twice the angle at the circumference.

• Angles in the same segment are equal.

• The angle in a semi-circle is always 90 degrees.

• The opposite angles in a cyclic quadrilateral always add up to 180 degrees.

• The angle between a circle and a tangent is equal to the angle in the alternate segment.

• The lengths from where two tangents touch a circle to where they meet each other are equal.

The following diagram shows some circle theorems: angle in a semicircle, angle between tangent and radius of a circle, angle at the centre of a circle is twice the angle at the circumference, angles in the same segment are equal, angles in opposite segments are supplementary; cyclic quadrilaterals and alternate segment theorem. Scroll down the page for more examples and solutions of circle theorems.

**Circle Theorem Basic definitions**

Chord, segment, sector, tangent, cyclic quadrilateral.

Theorem: Angle subtended at the centre of a circle is twice the angle at the circumference.**Circle Theorems part 1 of 2**

The angle between a radius and a tangent is 90 degrees.

The angle at the centre is twice the angle at the circumference.

Angles in the same segment are equal.

The angle in a semi-circle is always 90 degrees.

The opposite angles in a cyclic quadrilateral always add up to 180 degrees.**Circle Theorems part 2 of 2**

The angle between a circle and a tangent is equal to the angle in the alternate segment.

The lengths from where two tangents touch a circle to where they meet each other are equal.

More Lessons for GCSE Maths

Math Worksheets

Examples, solutions, and videos to help GCSE Maths students learn the circle theorems.

• Angle subtended at the centre of a circle is twice the angle at the circumference.

• The angle between a radius and a tangent is 90 degrees.

• The angle at the centre is twice the angle at the circumference.

• Angles in the same segment are equal.

• The angle in a semi-circle is always 90 degrees.

• The opposite angles in a cyclic quadrilateral always add up to 180 degrees.

• The angle between a circle and a tangent is equal to the angle in the alternate segment.

• The lengths from where two tangents touch a circle to where they meet each other are equal.

The following diagram shows some circle theorems: angle in a semicircle, angle between tangent and radius of a circle, angle at the centre of a circle is twice the angle at the circumference, angles in the same segment are equal, angles in opposite segments are supplementary; cyclic quadrilaterals and alternate segment theorem. Scroll down the page for more examples and solutions of circle theorems.

Chord, segment, sector, tangent, cyclic quadrilateral.

Theorem: Angle subtended at the centre of a circle is twice the angle at the circumference.

The angle between a radius and a tangent is 90 degrees.

The angle at the centre is twice the angle at the circumference.

Angles in the same segment are equal.

The angle in a semi-circle is always 90 degrees.

The opposite angles in a cyclic quadrilateral always add up to 180 degrees.

The angle between a circle and a tangent is equal to the angle in the alternate segment.

The lengths from where two tangents touch a circle to where they meet each other are equal.

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