Hi Forum.

I have been studying secant and tangent theorems for the circles and I found this question:

*Find the length of the common internal tangent segment of two circles with radii of 4 units and 12 units whose centers are 20 units apart.*
Ok, I drew a sketch and I tried to used secant tangent theorems but I didn't get it off the ground.

There's a formula that states

With

being the segment's length.

I can only think of ways of solving this, cutting the segment into two parts, that are not equal, and then summing them.

But I don't know how to put the distance of 20 units between the centers.

My question is, how do we get the formula

?

Thanks!

*Note that the x and the y in the formula are not the same x and y in the sketch.*
Here is a sketch: