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HELP 20 points Find x. x DO Radius = 10 Radius = 9 Enter a, b, c, d, or e. a. 19.9 b. 6/15 c. 18.01 d. 6/10 e. 185 Enter

HELP 20 points Find x. x DO Radius = 10 Radius = 9 Enter a, b, c, d, or e. a. 19.9 b-example-1
User ChangLi
by
3.2k points

1 Answer

23 votes
23 votes

Answer:

d. 6√10

Explanation:

You want the measure of x, the length of the mutual external tangent to circles A and B with radii 10 and 9, respectively.

Right triangle

Line segment D'B can be constructed parallel to DC through point B to form right triangle AD'B. The side lengths of that triangle are ...

  • hypotenuse AB = 10+9 = 19
  • short leg AD' = 10 -9 = 1
  • long leg D'B = x

The Pythagorean theorem tells us how to find x:

x² + 1² = 19²

x = √(361 -1) = √360 = 6√10

The length of x is 6√10, matching choice D.

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User Jared Shaver
by
3.1k points
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