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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