Circle problem! I need help!

[Xonian]

Ok, I am having some trouble with 24. If someone could help me out, that'd be great.

A circle can be drawn through points X, Y, and Z. XW=8, YW=6, ZW=12.

Find the radius of the circle, and the distance from the center to point W.

I know the answers, 5 root 5, and root 29, respectively. The problem is that I am having some trouble reaching those answers.

The problem is also attached.



Thanks! Please help ASAP!

 

[Xonian]

Anybody?

 

[Xonian]

Somebody...anybody...

 

[daon2]

I have never been "trained" in axiomatic geometry. But this is how I would solve it:

Say the cord is a perpendicular distance h from the center at (0,0). The cord has length 20. So the points X and Z lie at (-10, h) and (10,h). Point Y lies at (-2,6+h)

We have

\(\displaystyle 10^2+h^2 = r^2\)

and


\(\displaystyle (-2)^2+(6+h)^2 = r^2\)

Solving this simultaneous system we obtain \(\displaystyle h=5\) and \(\displaystyle r=5\sqrt{5}\)

I'm sure you can get b) now.

 

[mmm4444bot]

Ok, I am having some trouble with 24.

I am having some trouble reaching [the given] answers.

Please show us what you can do for the parts over which you are not having trouble.

Also, be sure to check out the forum guidelines and rules, before posting again. Here is a link to a summary page of the guidelines. (Links for the complete rules and guidelines appear near the bottom of the summary page.)

Thank you! :cool:

 

[Xonian]

I have never been "trained" in axiomatic geometry. But this is how I would solve it:

Say the cord is a perpendicular distance h from the center at (0,0). The cord has length 20. So the points X and Z lie at (-10, h) and (10,h). Point Y lies at (-2,6+h)

We have

\(\displaystyle 10^2+h^2 = r^2\)

and


\(\displaystyle (-2)^2+(6+h)^2 = r^2\)

Solving this simultaneous system we obtain \(\displaystyle h=5\) and \(\displaystyle r=5\sqrt{5}\)

I'm sure you can get b) now.

Thank you sir!