Subtended that is a funny word, but what does it mean?

We see this a lot in maths and it often confuses us and makes things seem more complicated than they actually are.

Subtended just means that the angle made at the circumference from the diameter.

Here you can see that it is a right angle. It is also within a semi circle.

Theorem

Every angle at the circumference of a semicircle that is subtended by the diameter of the semicircle is a right angle.

If you draw a straight line from each end of the diameter to hit the circumference of the circle you will see a right angle.

So it is the angle made from the diameter at the circumference. That is all it means.

Example

In the example find x.

We know that angles in a triangle add up to 180°

We know that the one angle is a right angle 90°

The angle given is 38°

180 - 90 - 38 = 52°

Have you noticed that circle theorems are just basic facts from our angle properties tool box?

Lets unlock it and use them.

Note: Circle theorem questions rarely show the right angle depicted by the square in the corner.