A, B and C lie on a circle with centre O. Angle AOB = 124°. Work out…

Step by step

The question

Question: find x.

The angle at the center is 124°.

The angle at the edge is x.

1 Use the circle rule

O is the center of the circle.

Lines from A and B to the center make the angle at the center.

Lines from A and B to C, on the edge, make the angle at the edge.

Both angles face the same arc: their arms end at A and B.

It is the orange part of the circle.

Circle rule: the angle at the center is double the angle at the edge, on the same arc.

This rule was proved long ago, from the equal radii.

It works in every circle.

So the angle at the edge is half of the angle at the center: x = 124/2.

124 divided by 2 is 62.

So x = 62.

2 Check

Let's check: double 62°.

124° is double 62°.

So x = 62 is right!

Let's look back.

First: use the circle rule.

Last: check.