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

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

step-by-step explanation: