SOLUTION: the distance between the centers of the two circles is 13 cm. If their radii are 5cm and 8cm, how long is their common external tangent segment? Thank you!

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Question 1205673: the distance between the centers of the two circles is 13 cm. If their radii are 5cm and 8cm, how long is their common external tangent segment?
Thank you!
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

If the radii of the circles are 5 cm and 8 cm and the distance between their centers is 13 cm,

then these circles touch each other and have only one common point, which is the tangent point.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let A be the center of the circle with radius 5cm and B be the center of the circle with radius 8cm.

Since the distance between the centers is 13cm, the two circles are tangent to each other.

Draw the common external tangent CD, with C and D being the points of tangency with circles A and B respectively. The radii AC and BD are both perpendicular to the tangent CD.

Let point E be on radius BD so that AE is parallel to the tangent CD. ACDE is then a rectangle, with one dimension 5 cm and the other dimension equal to the length of the common external tangent.

Use the Pythagorean Theorem on right triangle ABE to find the length of the other dimension of the rectangle and thus the length of the external common tangent.

x%5E2%2B3%5E2=13%5E2
x%5E2%2B9=169
x%5E2=160
x=sqrt%28160%29=4%2Asqrt%2810%29

ANSWER: 4%2Asqrt%2810%29cm