Finding two diametres |$AC$| and |$AD$| where $B$ is the center of the larger one and both the circle touch the point $A$.

Question

Two circle as shown in the figure, A is the tangent point of both the circle. B is the centre of the large circle. The distance of CD = 90 mm(according to estimation) and EF = 50 mm. What is the value of diametre of both the circle?

I couldn't catch the right process although I tried with some steps. But what I figured out wasn't so usefull at all. I need some help to solve the problem.

Thanks in advance.

Answer 1

$AB = r$, $BC = r - 90$, $EB = r - 50$

By power of a point, $$ AB\cdot BC = EB^2 $$ and from this equation $r$ can be found.