external tangent to two circles

Hi ! Glad I've found this forum. I've been having a headache with this question.

Find the length of the common external tangent to two circles of radii 5 cm and 12 cm, respectively if the distance between their centers is 25 cm.

According to the textbook, the answer is 24 cm. I am getting an answer of 27 by basic trigo functions. Can any genius out there solve this ?

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Originally Posted by redpilot1234

Hi ! Glad I've found this forum. I've been having a headache with this question.

Find the length of the common external tangent to two circles of radii 5 cm and 12 cm, respectively if the distance between their centers is 25 cm.

According to the textbook, the answer is 24 cm. I am getting an answer of 27 by basic trigo functions. Can any genius out there solve this ?

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1. The bad news first: The book is right.

2. You don't need any trigonometric functions but simple Pythagorean theorem: The length of the tangent is one leg of a right triangle whose hypotenuse is 25 and whose first leg is 12 - 5 = 7.

Wow. Nice presentation ! So you're one of the geniuses here ... btw, what software did you use to draw that ? It would definitely help me in analyzing problems. Thanks !!!