SOLUTION: Two wheels of radius 15.98cm and 13.67cm respectively rest on the ground. If the centers of the wheels are 33.73cm apart, how far apart are the points where they touch the ground?

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Question 369847: Two wheels of radius 15.98cm and 13.67cm respectively rest on the ground. If the centers of the wheels are 33.73cm apart, how far apart are the points where they touch the ground?
Answer by jsmallt9(3758) (Show Source):
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It may help to draw a picture of the problem. Draw two circle, one larger than the other. Let's label the center of the larger circle A and the center of the smaller circle B. Next, draw a line segment straight down from A to a point which has the same height as B.

We now have a right triangle ABC (with the right angle at C. We are told that the distance between the centers is 33.73cm. On our right triangle this would be the hypotenuse, AB. We are also told that the radii of the wheels are 15.98 and 13.67. Since C has the same height as B, it also is 13.67cm from the ground. This makes AC = 15.98cm - 13.67cm = 2.31cm. The third side of our right triangle is BC. We can find BC using the Pythagorean Theorem:

Simplifying...

Find the square root of each side (and discarding the negative square root since BC cannot be negative):

If you look at your drawing you will see that the length of BC is the same as the distance between where the the tires touch the ground. (If you don;t see this, draw line segments down from each center all the way to the ground and label the point on the ground below A as "D" and the point on the ground below B as "E". You now have a rectangle BCED. And opposite sides of rectangles, like BC and DE, are always congruent.)

So the answer to the problem is cm. This is an exact answer. Use your calculator on the square root if you want a decimal approximation.