Basic Circle Questions

[rickjames]

1. A, B and C are points on the circumference of a circle, centre O, and ∠BAC=115°. Calculate the number of degrees in ∠OBC.

 

I drew a diagram but could not come up with anything primarily because ∠BAC and centre O lie on opposite sides of chord BC (draw a quick diagram if you don't know what I mean).

 

2. ABCD is a quadrilateral inscribed in a circle and AB = CD. Prove that AC = BD.

 

This is pretty simple I think, if AB = CD, then BC = DA (do I need to say why?). Then just use Pythag to prove the diagonals are equal.

[s pepperchin]

1. A' date=' B and C are points on the circumference of a circle, centre O, and ∠BAC=115°. Calculate the number of degrees in ∠OBC.

 

I drew a diagram but could not come up with anything primarily because ∠BAC and centre O lie on opposite sides of chord BC (draw a quick diagram if you don't know what I mean).

 

2. ABCD is a quadrilateral inscribed in a circle and AB = CD. Prove that AC = BD.

 

This is pretty simple I think, if AB = CD, then BC = DA (do I need to say why?). Then just use Pythag to prove the diagonals are equal.[/quote']

 

For the first problem you need to look at al of the geometric relations you can get from circles as well as triangles.

 

For the second problem you can't assume that bc = da.

 

You should go into more detail about how you are doing the problem. They are both possible.

[taxpo]

I mean the same like s pepperchin

[the tree]

[math]

\setlength{\unitlength}{1cm}

\begin{picture}(4,4)

\thicklines

 

\put(2,3){\line(-2,-5){1}}

\put(1,1)

\put(2,2){$O$}

\put(4.05,1.9){$B$}

\put(1.7,2.95){$C$}

\put(3,2.8){$AB^2 = AC^2 + BC^2$}

\end{picture}

[/math]