A circle with a radius of 2 units has its center at (0, 0). A circle with a radius of 7 units has its center at (15, 0). A line tangent to both circles intersects the x-axis at (x, 0) to the right of the origin. What is the value of x?

ddocm Mar 7, 2021

#1**+1 **

The green line has a length of 2, the blue line has a length of 7, and the red line has a length of 15.

Since the green line is parallel to the blue line, the 2 right triangles shown above must be similar to each other.

That means the smaller red length is just \(\frac{2}{9}\cdot15 = \boxed{\frac{10}{3}}\), which is the answer.

textot Mar 7, 2021