GCSE Maths (AQA)

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Angle at Centre & Circumference

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Geometry and Measures Properties and Constructions

Angle at Centre & Circumference

5:29 More Circle Theorems
Spec G10
Previous Pyramids & Cones Next Triangle from a Diameter
  • The angle at the center of a circle is twice the angle at the circumference subtended by the same arc
  • A diameter splits the angles at the circumference and center of the circle
  • The lines from the center of the circle to the circumference are equal in length
  • Triangle OAC is an isosceles triangle, with angle OAC equal to angle OCA
  • Angle COA is equal to 180 degrees minus 2x
  • Angle AOD is equal to 2x
  • Triangle OBC is also an isosceles triangle, with angle BOD equal to 2y
  • The angle at the circumference (angle ACB) is equal to X + Y
  • The angle at the center (angle AOB) is equal to 2X + 2Y, which can be factorized to 2 times angle ACB
  • This proves the circle theorem that the angle subtended at the center of a circle is twice the angle subtended at the circumference

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