Answer:
8√3 ≈ 13.86
Step-by-step explanation:
You want the length of the external tangent to circles with radii 5 and 7 units spaced 14 units apart.
The length of the external tangent is the long leg of the right triangle with short leg equal to the difference in radii, and with hypotenuse equal to the spacing between the circles. The Pythagorean theorem can find the required length:
x² +2² = 14²
x² = 196 -4 = 192
x = √192 = 8√3
The length of the common external tangent is 8√3 units, about 13.86 units.
