A theorem is a statement that can be proved using known mathematical facts and reasoning.

An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.

A chord is any line segment joining two points on the circumference of a circle.

Two segments are created when dividing a circle into two parts using a chord.

The angles in the same segment are equal

Maths

In the prior unit, pupils applied their understanding of angles to solve increasingly complex problems. In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

Circle theorems

Find the size of angle $$x$$° on this 18-point geoboard.

Find the size of angle $$y$$° on this 18-point geoboard (in degrees).

The image shows an 18 point geoboard. The size of the angle labelled $$z$$° is {{}}°.

Both ∠ACB and ∠ADB are angles at the circumference subtended by the chord AB. 
The size of the angle labelled $$k$$° is {{}}°.

Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF. 
The size of the angle labelled $$p$$° is {{}}°.

Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK. 

The size of the angle labelled $$t$$° is {{}}°.

An angle at the circumference of a circle is subtended by the diameter of that circle.
What is the size of this angle (in degrees)?

The size of the angle labelled $$x$$° is {{}}°.

The size of the angle labelled $$y$$° is {{}}°.

The size of the angle labelled $$z$$° is {{}}°.

The image shows a circle with centre O. A triangle is formed from two radii and a chord. A tangent to the circle is shown. The size of the angle labelled $$a$$° is {{}}°. 

Find the size of angle $$b$$° (in degrees).

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