Circle Theorems: Solving for Unknown Angles in Isosceles Triangles

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Homework Help Overview

The discussion revolves around circle theorems and their application to finding unknown angles in isosceles triangles, specifically angles ABC and CBO in relation to a given diagram.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore relationships between angles in cyclic quadrilaterals and inquire about the properties of angles in isosceles triangles. There are questions regarding the specific angles and arcs involved, as well as the implications of the triangle being inscribed in a circle.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on angle relationships and seeking clarification on the diagram. Some guidance has been offered regarding the properties of isosceles triangles and cyclic quadrilaterals, but no consensus has been reached on the specific values of the angles.

Contextual Notes

Participants mention the need for a diagram to aid understanding, and there are constraints regarding the approval of shared resources. The original poster expresses confusion about the angles and their relationships, indicating a need for further exploration of the topic.

grahammm
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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
 

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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

Do you have the answer?
 

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