Circle problem

[mathwannabe]

Hello everybody



The problem is on the picture. Any hints that could lead me to solution?

EDITED: I am adding the text of the problem... just in case.

Two circles are touching each other in one point. Both circles have radius r = 4cm. Third circle is touching both circles and their mutual tangent. What is the radius of the third circle?

 

[wjm11]

Draw a line through the center of the small circle that is parallel to the top (horizontal) tangent line.
Draw line segments from the centers of the large circles to the center of the small circle.
Use the Pythagorean theorem.

 

[pka]

Hello everybody

View attachment 2016

The problem is on the picture. Any hints that could lead me to solution?

There is a beautifully simple answer but you must work for it.
Join the centers of the large circles.
Extend the radial segment of the small circle to meet the first segment.
Call the length of that extension \(\displaystyle s\).

Now \(\displaystyle 2r+s=4~\&~(4+r)^2=16+(r+s)^2\). Where do those come from?

Solve for \(\displaystyle r\).

 

[mathwannabe]

I think I got it... Thank you all