Circle Theorems

Work out the missing angles. The angles you have to find are the letters printed in blue. Every dot in the middle of a circle is its centre.

These are the rules you need:

  • The angle at the centre is twice the angle at the circumference standing on the same arc.
  • Angles standing on the same arc, in the same segment, are equal.
  • The angle in a semicircle is 90°.
  • The opposite angles of a cyclic quadrilateral add up to 180°.
  • Two radii make an isosceles triangle, so its two base angles are equal.

Reload the page and you get a new worksheet - the angles are generated at random every time.


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