Maths - Circle Theorems

grahammm

Hi,

I am really confused with circle theorems, attached is a diagram and I need to find out ABC and CBO.

I have worked out that angle ACB is x degrees, and also know that angle OAC is equal to angle OBC.

But I don't know how to work out the what either are

Thanks

Graham

Attached Thumbnails

 

grahammm

Is this something to do with opposite angles on a cyclic quadratic add up to 180?

whozum

If youcan post it on the web somewhere, we'd be able to see it before tomorrow. It has to be pre approved.

grahammm

See www.kgmm.co.uk/maths.GIF

Many thanks!

Graham

whozum

Arc ABC? Angle ABC? You didnt label this angle.


Do you know anything specific about the inscription of the triangle in the circle? I want to say that the arcs between A B and C are 120 degrees, but I can't tell if thats whatits supposed to be.

grahammm

Find in terms of X, expressions for the angles:

- ABC
- CBO

The points A,B, and C lie on the centre circle O.

whozum

Since AC = BC, the triangle ABC is isosceles, and angles ABC and BAC are equal. The sum of all three angles is 180.
Where y is angle ABC
180 = 2y+x
y = 90-x/2

Do you have the answer?