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.

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

A tangent of a circle is a line that intersects the circle exactly once.

The alternate segment theorem

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 $$a$$° (in degrees).

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

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

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

∠ATC = 46°
∠ABT is subtended by the chord AT.
Find the size of angle $$e$$° (in degrees).

∠PEF is subtended by the chord PF.
∠PFE is subtended by the chord PE.
Find ∠EPD (in degrees).

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 {{}}°. 

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

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