Geometry and measuresGCSE Higher / IGCSE Extended

Radii of the same circle are equal, forming an isosceles triangle

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

  • Use the equal base angles of triangle . The centre angle and both base angles add to 180 degrees.

The theorem

All radii of the same circle are equal. Two radii and a chord form an isosceles triangle.

Example 1

With numerical values

is the centre. Find the angle .

Equal radii make triangle isosceles, so its base angles are equal.

Example 2

With algebra

is the centre. Find . Each labelled expression is an angle in degrees.

Equal radii make triangle isosceles, so its base angles are equal.Collect like terms.
Substitute the value of .
Labelled angles

Your turn

Question 1

Find angle .

Check answer
Equal radii make triangle isosceles, so its base angles are equal.
Question 2

Find the value of .

Check answer
Equal radii make triangle isosceles, so its base angles are equal.Collect like terms.
Substitute the value of .
Labelled angles
Question 3

Find angle .

Check answer
Equal radii make triangle isosceles, so its base angles are equal.
Question 4

Find the value of .

Check answer
Equal radii make triangle isosceles, so its base angles are equal.Collect like terms.
Substitute the value of .
Labelled angles
Question 5

Find angle .

Check answer
Equal radii make triangle isosceles, so its base angles are equal.
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