SOLUTION: http://jasper.kaptest.com/content/media/00/124700.11.25cbb913-01d3-4258-af2b-5415d367e71e.png In the figure above, AC is tangent at point B to the circle centered at O. DFis pa

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: http://jasper.kaptest.com/content/media/00/124700.11.25cbb913-01d3-4258-af2b-5415d367e71e.png In the figure above, AC is tangent at point B to the circle centered at O. DFis pa      Log On


   

Question 955754: http://jasper.kaptest.com/content/media/00/124700.11.25cbb913-01d3-4258-af2b-5415d367e71e.png
In the figure above, AC is tangent at point B to the circle centered at O. DFis parallel to AC . If DF=6sqrt 3 and the circumference of the circle is 12π, what is the probability that a point randomly selected from the interior of the circle will fall within the shaded region?


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the circumference,
12pi=pi%2A%282%2AOD%29
OD=6
and since DE=%281%2F2%29DF=3sqrt%283%29
and
sin%28theta%29=DE%2FOD
sin%28theta%29=%283sqrt%283%29%29%2F6
sin%28theta%29=sqrt%283%29%2F2
theta=60
So the shaded region takes up 120 degrees of the 360 degree circle total.
P=120%2F360=1%2F3