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Circle Theorems



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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.

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.


 

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