The Math Meridian
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Circle theorems

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Learn it Key circle theorems: the angle at the centre is twice the angle at the circle on the same arc; the angle in a semicircle is $90°$; angles in the same segment are equal; opposite angles of a cyclic quadrilateral add to $180°$; a tangent is perpendicular to the radius; two tangents from one point are equal.

Example: O is the centre and $\angle ACB = 35°$. Find $\angle AOB$.

  1. Both angles stand on arc AB.
  2. Angle at the centre = 2 × angle at the circle.
  3. $\angle AOB = 70°$.

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