Angle in a Semicircle (OCR GCSE Maths): Revision Note

Angle in a Semicircle

Circle Theorem: The angle in a semicircle is 90°

• The lines drawn from a point on the circumference to either end of a diameter are perpendicular

  • The angle at that point on the circumference is 90°

  • This circle theorem only uses half of the circle

    • The right-angle is called the angle in a semicircle

• This is a special case of the circle theorem "the angle at the centre is twice the angle at the circumference"

  • The angle on the diameter is 180°

  • The angle at the circumference is halved, giving 90°

• To spot this circle theorem on a diagram look for a triangle where

  • one side is the diameter

    • Remember that a diameter always goes through the centre

  • all three vertices are on the circumference

• The 90º angle will always be the angle opposite the diameter

• When explaining this theorem in an exam you must use the keywords: 

  • The angle in a semicircle is 90° 

• Questions that use this theorem may

  • appear in whole circles or in semicircles

  • require the use of Pythagoras' Theorem to find a missing length