SOLUTION: How do you find the tangent segment AB when O to O' is 12, the radius for O is 5 and O' is 3 and B to O is 3? PS I need it by today 10 PM

Algebra ->  Pythagorean-theorem -> SOLUTION: How do you find the tangent segment AB when O to O' is 12, the radius for O is 5 and O' is 3 and B to O is 3? PS I need it by today 10 PM      Log On


   

Question 1066762: How do you find the tangent segment AB when O to O' is 12, the radius for O is 5 and O' is 3 and B to O is 3?
PS I need it by today 10 PM
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I hope you live in California, because it is past 11 PM on the East coast.
I am guessing what the meaning of yoir question is.
I think you are talking about a line tangent to two circles with centers 12 units apart,
with radius 5 and 3 units.
The circles, with a tangent line, the radii to the tangency points,
and the line going through both centers are drawn below.
I assume A and B are the tangency points,
and you want to find the distance between them.

In the drawing you see two similar right triangles.
The short legs measure 5, and 3 (the circles' radii).
Because the triangles are similar,
the ratio of hypotenuse to long leg is similar for both, so
x%2F3=%2812%2Bx%29%2F5--->5x=3%2812%2Bx%29--->5x=36%2B3x--->5x-3x=36--->2x=36 ---> x=36%2F2--->x=18
Know that we know x, we can use the Pythagorean theorem,
with the hypotenuse and short leg of both triangles to found the long legs.
For the small triangle:
BP%5E2%2B3%5E2=18%5E2-->BP%5E2%2B9=324-->BP%5E2=324-9-->BP%5E2=315-->BP=sqrt%28315%29=SQRT%289%2A35%29=3SQRT%2835%29 .
For the large triangle:
AP%5E2%2B5%5E2=%2812%2B18%29%5E2-->AP%5E2%2B5%5E2=30%5E2-->AP%5E2%2B25=900-->AP%5E2=900-25-->AP%5E2=875-->AP=sqrt%28875%29=sqrt%2825%2A35%29=5sqrt%2835%29 .
So,
AB=AP-BP=5sqrt%2835%29-3sqrt%2835%29=highlight%282sqrt%2835%29%29 .
Did I guess right?