02 – Rule 1

Angle at centre is twice that at circumference:

Prove that the angle subtended by an arc at the centre (2b) is twice the angle subtended at the circumference (b).

Hint: Draw a line from the centre o, to the point where the two lines cross the circumference at the top of the diagram

Draw a line, one radius long to split the triangle into two isosceles triangles as shown

Mark the angles b and c for each isosceles triangles.

Work out the other angles in each triangle

Work out the angle left at the centre. 360° – (180°–2b) – (180°–2c) = 2(b+c)

i.e. twice the angle at the circumference

Your Turn:

Find the value of x

 

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