*the angle subtended by a chord of a circle at the centre of the circle is twice that subtended by the same chord at the circumference.*Perhaps a diagram might make things much easier:

The

**is the line**

*chord***, and the**

*AB***is the angle**

*angle subtended at the centre***, and the**

*AOB***is the angle**

*angle subtended at the circumference***, as indicated in Greek above, haha. So this property of a circle says that angle**

*ACB***is twice that of angle**

*AOB***. But why?**

*ACB*Easy enough, I shall use the method that Shaun used during our lecture, which is a rather neat and easy proof; so kudos to Shaun! First of all, you divide the triangle

**into half, down the centre as shown below with a line**

*ABC***, and then notice I've coloured an isoceles triangle in green:**

*CD*And then you should notice that this line should bisect the angles ** AOB** and

**, and we can conclude first that:**

*ACB*

And from this, the following statements should therefore make sense:

Quite a neat proof huh? Shaun came up with it all by himself** , pro**!

## 1 comment:

I didn't come up with it...

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