Find the distance between the two circles?

Question

The centers of two circles, with radii 6 cm and 36 cm, are 50 cm apart.

Answer 1

If the circles were touching each other, their centers would be 6 + 36 cm apart = 42 cm. So there must be 8 cm "space" between the two circles to cause the centers to be 50 cm apart.

Answer 2

Imagine the two circles beside each other with the centers of each circle marked with a dot. From one dot to the other is 50 cm.
Imagine a straight line drawn from center to center. This line is 50 cm. One of the circles, we know part of that line is 6 cm. We also know that in other circle part of that same line is 36 cm. So, we have 6 cm + 36 cm + the middle section of the line which is not in the circles, all = 50 cm

6 + 36 = 42, We need 8 more cm to make 50. That space between the 2 circles is 8 cm

I hope I have explained it well enough so that you can visualize the diagram and understand how to do it.

Answer 3

If you draw radii from the center of each circle, perpendicular to the common external tangent, you will see a trapezoid, with legs 8 and 3 and altitude 12. Now draw a segment parallel to the common external tangent, from the center of the smaller circle, and you will see a right triangle with legs 5 and 12. The hypotenuse, which is the distance between the circles, is 13.

Answer 4

The line of centers is 50cm.
Thus the circles are separated by a distance of
50 - 6 -36 = 8cm

Answer 5

distance = 50 - 6 - 36 = 8cm

Answer 6

50-36-6 = 8cm apart