Circle Theorems

Angles at Centre -  Circle Theorem:

The angle subtended by an arc at the centre is twice the angle at the circumference

How to spot the angles at centre circle theorem:

STEP 1  \n Find any two radii in the circle and follow them to the circumference  \n STEP 2 \n See if there are lines from those points going to any other point on the circumference

What to say in an exam if asked the reason for the angles at centre circle theorem:

The angle at the centre is twice the angle at the circumference

Angles at Circumference - Circle Theorem:

The angle in a semicircle is a right angle

How to spot the angles at circumference circle theorem:

Look for a diameter in the circle and see if it makes the base of a triangle, with its top vertex at the circumference

• Make sure that you are looking at a diameter by checking it goes through the centre

• These questions only need half of the circle so they could appear in whole circles or in semicircles only

What to say in an exam if asked the reason for the angles at circumference circle theorem:

The angle in a semicircle is 90°