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.

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Question 315355: 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.
please help final tomorrow!!!!

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!



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

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