Answer:
4[tex]\sqrt{3}[/tex] 0r 6.93 units
Step-by-step explanation:
Let's draw the figure using the given information.
Draw a perpendicular line from the center of the smaller circle to radius of bigger circle. Then it forms a rectangle with x by 2.
As you can see it formed a right triangle with the base x, legs measures 4 and 8 (6 + 2).
Now we can find the value of the base (x) using the Pythagorean theorem.
The values of x is the same as the length of external tangent AB.
The Pythagorean theorem states the square of the hypotenuse is equal the sum of the squares of their legs.
So, [tex]8^2 = x^2 + 4^2[/tex]
[tex]x^2 + 16 = 64[/tex]
[tex]x^2 = 64 -16\\x^2 = 48[/tex]
Taking square on both sides, we get
x = [tex]\sqrt{16*3}[/tex]
x = 4[tex]\sqrt{3}[/tex] 0r 6.93 units
Therefore, the length of external tangent AB is 4[tex]\sqrt{3}[/tex] 0r 6.93 units
