SOLUTION: The centers of two circles with radii of 3 and 5 are 17 units apart. Find the length of the common internal tangent. Answer either in exact form or rounded to the nearest tenth.

Given AC=3, BD=5, AB=17

Need to find internal tangent CD

Extend radius AC by 5 units to E, where CE is 5 units long.
then Draw BE, so that CDBE is a rectangle.



Now triangle ABE is a right triangle, with shorter leg AE = 3+5 = 8,
and hypotenuse AB which is given to be 17.

So by the Pythagorean theorem,








And since CDBE is a rectangle, CD = EB = 15

So the internal tangent, CD, is 15 units.

Edwin