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Problem: Points A and B are the endpoints of a diameter of a circle with center C. Points D and E lie on the same diameter so that C bisects segment DE. Let F be a randomly chosen point within the circle. The probability that triangle DEF has a perimeter less than the length of the diameter of the circle is 17/128. There are relatively prime positive integers m and n so that the ratio of DE to AB is m/n . Find m + n.
I approached this problem by spitting the circle in two halves with diameter AB and then again halving the circle by drawing a perpendicular XC to AB. Now the problem becomes finding CE/CB given that the probability that XB<CB is 17/128. I can't work out the solution from here..