A bicycle chain fits tightly around two gears. What is the distance between the centers of the gears if the radii of the bigger and smaller gears are 9.3 inches and 2.4 inches, respectively, and the portion of the chain tangent to the two gears is 26.5 inches long?
See the following diagram :
Let AC = 9.3
Let CE = AC - BD = 9.3 - 2.4 = 6.9
Let AB = 26.5 = ED
So.....we have right triangle DEC with legs ED and EC
And the hypotenuse (CD) is the distance we are looking for = sqrt ( ED^2 + EC^2) =
sqrt (26.5^2 + 6.9^2) ≈ 27.38 in