# Proving . . .

• Jan 8th 2010, 04:28 AM
x-mather
Proving . . .
Circle k(S; r)is touching point A of line AB. Circle l(T; s)is touching point B of line AB and intersects circle k in the edge points C, D of its diameter. Prove that the intersection M of lines CD and AB is the centre of line AB.
• Jan 8th 2010, 01:29 PM
Henryt999
Trying to help but...
Hi!
Reading the problem over and over and canīt quite grash it. C;D are antipods of large circle? And inside that circle are two other circles?
• Jan 9th 2010, 07:41 AM
x-mather
See this (I know it is not accurate but it helps)

http://content.imagesocket.com/thumbs/sssssss723.JPG
• Jan 10th 2010, 05:03 AM
x-mather
If you know it, written form will be sufficient for me.
• Jan 10th 2010, 05:50 AM
Here is a sketch of the geometry.

The large blue circle has the same radius as circle k.
Using the radius of the smaller circle,
next draw right-angled triangles to show |TF|=|TG|.

The show |BM|=|BA|

I had to shrink my sketch and it has become a little skewed.
Those lines are meant to be perpendicular.

This only works if CD is a centreline.
• Jan 10th 2010, 05:54 AM
Henryt999
Well, does this make sence
Is this somewhat understandable?
• Jan 10th 2010, 06:07 AM