radius of circle inscribed in rectangle

Question

I have two circles inside a rectangle(4 * 6), where the diameter of one of both is the total length of a side of the rectangle, and the other circle diameter is part of the length of the another side.

This image resume all:

• What is the name of the theory behind this problem?
• How to find the radius R?

Answer 1

Hint

Draw a line between the circle centers. Note that the length is exactly $R+2$. Thus:

$$(R+2)^2=2^2 + (6-R)^2$$ Can you take it from there?

Answer 2

Hint: note the right triangle below. What does this tell you about $R$?