# Tangent Circles

#### cw86

I need to know how to calculate the length of radius a with only knowing the length of radius b and the value of variable x in the picture below

#### bjhopper

I need to know how to calculate the length of radius a with only knowing the length of radius b and the value of variable x in the picture below

View attachment 16837
Hi cw86,
Tangent at E is perpendicular to AE and BE therefore AEB is a straight line.Draw aline parallel to line x thru B.
( a+b)^2= ( a-b)^2 +x^2 Solution of this equation gives 4ab =x^2
x= sqrt 4ab= 2sqrt ab

bjh