Two circles have radii of 10 and 15. If the length of their common external tangent is 12, Find the distance between the centers of the circles.

4\sqrt{3}

3

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, 8^2 = x^2 + 4^28

2

=x

2

+4

2

x^2 + 16 = 64x

2

+16=64

\begin{gathered}x^2 = 64 -16\\x^2 = 48\end{gathered}

x

2

=64−16

x

2

=48

Taking square on both sides, we get

x = \sqrt{16*3}

16∗3

x = 4\sqrt{3}

3

0r 6.93 units

Therefore, the length of external tangent AB is 4\sqrt{3}

3

0r 6.93 units

ok then what happened.

a.)the line for function b is steeper