circle theorems

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7 Terms

1
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alternate segment theorem

  • angle that lies between a tangent

  • and a chord

  • is equal to the angle subtended by the same chord

  • in the alternate segment

<ul><li><p>angle that lies between a tangent</p></li><li><p>and a chord</p></li><li><p>is equal to the angle subtended by the same chord</p></li><li><p>in the alternate segment</p></li></ul><p></p>
2
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tangent of a circle theorem

  • angle between a tangent

  • and a radius

  • is always 90°

  • tangents which meet at the same point

  • are equal in length

<ul><li><p>angle between a tangent</p></li><li><p>and a radius</p></li><li><p>is always 90°</p></li></ul><p></p><ul><li><p>tangents which meet at the same point</p></li><li><p>are equal in length</p></li></ul><p></p>
3
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chord of a circle theorem

  • angle between

  • the midpoint of a chord

  • and the radius

  • is always 90°

<ul><li><p>angle between</p></li><li><p>the midpoint of a chord</p></li><li><p>and the radius</p></li><li><p>is always 90<span>°</span></p></li></ul><p></p>
4
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angles at the centre theorem

  • angles at the circumference

  • are half

  • angles at the centre

<ul><li><p>angles at the circumference</p></li><li><p>are half</p></li><li><p>angles at the centre</p></li></ul><p></p>
5
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angles in a semi-circle theorem

  • angles in semi-circles

  • are always 90°

6
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cyclic quadrilateral theorem

  • opposite angles

  • in a cyclical quadrilateral

  • always add up to 180°

<ul><li><p>opposite angles</p></li><li><p>in a cyclical quadrilateral</p></li><li><p>always add up to 180°</p></li></ul><p></p>
7
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angles in the same segment theorem

  • angles in the same segment

  • are equal

<ul><li><p>angles in the same segment</p></li><li><p>are equal</p></li></ul><p></p>