Jurgenson Geometry Circle chapter question

[Kendall]

Jurgenson Geometry   My text is from 1985, but I know a lot of the problems are in the newer books as well.

 

Circle chapter

 

Section called : Circles and lengths of segments

 

This is the last B question in my book and says : A circle can be drawn through points X, Y, and Z       W is between X and Z  XW=8 WZ=12   YW is perpendicular to XZ at W  YW=6     There is a drawing of the segments that I have described.

 

What is the radius of the circle?

 

I’m stuck.  I don't have a solution book.  I do have the answer.  

 

I know I am just not seeing something. 

 

Thanks in advance for any help you can give me.

 

Kendall 

[RootAnn]

They've drawn the circle in the solutions manual. They've also made a point Q which is on the XZ chord and directly above the circle's center, O (not shown in your diagram). So, OQ is perpendicular to XZ. 

I think they are using theorem 9-11 to find the other part of the chord that starts at Y and ends at the other end of the circle. (6x=8x12)

 

They then point out that diameters bisect both segments so that XQ=QZ=10. They figure WQ, YP (where P is on the chord that starts at Y and ends at the other end of the circle. OP is perpendicular to that chord), and WP.

They find OZ and WO.

 

Does that get you started or just get you more confused? I think the key is to work on your figure & use theorem 9-11 to get started.

Edited January 27, 2017 by RootAnn

[Kendall]

Thank you!  I had done the first two things, but hadn't gone back and drawn the diameter to the vertical chord. I knew I was close.  I wanted to try one more time, but these children need me to actually homeschool them all day and they keep wanting to eat everyday...  

 

I think I'll give the problem to my married son to work with his sister when he is here this weekend:).