SOLUTION: The distance between the centeres of two circles with radii 9cm and 16cm is 25cm. The length of the segment of the tangent between them is?

Question 981200: The distance between the centeres of two circles with radii 9cm and 16cm is 25cm. The length of the segment of the tangent between them is?
Answer by josgarithmetic(39631) (Show Source): You can put this solution on YOUR website!
( I have a diagram, or picture for this, but may have a very long delay in making it available on the site).

Try to draw this figure. The tangent to the two circles will be perpendicular to the radii of both circles. You have a trapezoid of these lengths:
25, distance between centers;
9, radius of small circle;
16, radius of big circle;
u, unknown length of tangent segment.

This is like a rectangle WITH A MISSING TRIANGLE PIECE.
If you extend the 9 length radius side, and the missing side opposite of u is added, then you will have added a triangle with (RIGHT TRIANGLE) with leg 16-9=7, and hypotenuse 25. There, you should see, your value of a u the leg of this right triangle and is also the same measure as the tangent segment.

Again, reminder that you are looking for the value of u.

and you can solve this for u.
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