# Circle Theorems: Solving for Unknown Angles in Isosceles Triangles

• grahammm
In summary, in this conversation, the topic being discussed is circle theorems and finding the values of angles ABC and CBO. The given diagram shows a triangle inscribed in a circle, with the points A, B, and C lying on the circle's centre O. The conversation includes discussions about the angles and arcs of the triangle, as well as the fact that the triangle is isosceles. The final result is that angle ABC can be expressed as 90-x/2, where x is a given value, and the sum of all three angles is equal to 180 degrees.
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

#### Attachments

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

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

See www.kgmm.co.uk/maths.GIF[/URL]

Many thanks!

Graham

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

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 that's whatits supposed to be.

Find in terms of X, expressions for the angles:

- ABC
- CBO

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

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

## 1. What are circle theorems?

Circle theorems are a set of mathematical rules that relate to circles and the properties of their elements, such as chords, tangents, and radii.

## 2. How many circle theorems are there?

There are 6 main circle theorems, but there are also variations and extensions of these theorems that can be applied to different situations.

## 3. What is the most important circle theorem?

The most important circle theorem is probably the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

## 4. How can circle theorems be applied in real life?

Circle theorems are often used in engineering and architecture to design and construct circular structures such as roads, bridges, and buildings. They are also used in physics and astronomy to understand the motion and properties of circular objects.

## 5. Are there any tricks for remembering circle theorems?

One trick for remembering circle theorems is to use acronyms or mnemonics, such as SOHCAHTOA for remembering trigonometric ratios, or "All Students Take Calculus" for remembering the order of operations in algebra. Another helpful tip is to practice regularly and use visual aids, such as diagrams, to understand and remember the theorems.

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