Geometry and measuresGCSE Higher

The angle subtended by a diameter at the circumference is a right angle

Recognise the theorem, follow two examples, then try five questions.

  • must be a diameter, with the third vertex on the circumference.

The theorem

The angle subtended by a diameter at the circumference is a right angle.

Example 1

With numerical values

is a diameter. Find the angle .

An angle in a semicircle is 90 degrees.

Example 2

With algebra

is a diameter. Find . Each labelled expression is an angle in degrees.

An angle in a semicircle is 90 degrees.Collect like terms.
Substitute the value of .
Labelled angles

Your turn

Question 1

Find angle .

Check answer
An angle in a semicircle is 90 degrees.
Question 2

Find the value of .

Check answer
An angle in a semicircle is 90 degrees.Collect like terms.
Substitute the value of .
Labelled angles
Question 3

Find angle .

Check answer
An angle in a semicircle is 90 degrees.
Question 4

Find the value of .

Check answer
An angle in a semicircle is 90 degrees.Collect like terms.
Substitute the value of .
Labelled angles
Question 5

Find angle .

Check answer
An angle in a semicircle is 90 degrees.
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