Problem involving circles and tangents

[LTWaffles86]

Two circles, one with a radius of 6 and one with a radius of 2, have a common tangent with a length of 17. What is the distance between the circles' centers?
https://ibb.co/ph2Tdy6

I've been stuck on this for about 45 minutes with no progress. I tried to see if I could make some right triangles, but that didn't seem to work. Since then I haven't known what to try, just been staring at it thinking of what to do.

 

[jonah2.0]

Beer induced suggestion follows.

Two circles, one with a radius of 6 and one with a radius of 2, have a common tangent with a length of 17. What is the distance between the circles' centers?
https://ibb.co/ph2Tdy6

I've been stuck on this for about 45 minutes with no progress. I tried to see if I could make some right triangles, but that didn't seem to work. Since then I haven't known what to try, just been staring at it thinking of what to do.

You just need to reorient your diagram and use the distance formula.

LTWaffles86 Problem involving circles and tangents

www.desmos.com

 

[lev888]

Yes, you need a right triangle. The one where the distance segment is the hypotenuse.

 

[LTWaffles86]

Thank you so much! It makes more sense when you look at it like that.

 

[Steven G]

Draw a line that segment is parallel to CD and and goes from B to the line AC.