The tangent at any point on a circle is perpendicular to the radius at that point

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

The size of the angle labelled $$x$$° on this 9-point geoboard is {{}}°.

Find ∠OAB on this 9-point geoboard (in degrees).

Find ∠EFO on this 8-point geoboard (in degrees).

Find ∠DEF on this 8-point geoboard (in degrees).

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

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

The {{}} is a line which intersects the circle exactly once.

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

MY = 8 cm, 
OZ = 13 cm, 
ZM = 12 cm, 
OM = 5 cm.
Find the distance MX.

The size of the angle labelled $$m$$° is {{}}° (in degrees).

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

The angle subtended from arc AB at the circumference of the circle is 11°.  
Find ∠BOA (in degrees).

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