Quote:
Originally Posted by crushkiller
3.Points A, B and C are randomly selected on the circumference of a circle. What is the probability of angle ABC being acute?
Options :1/4,3/4,1/2,3/5
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i assume there is no frame of reference for the circle.. i.e. only the relative positions of A, B, C matter and neither of A B C coincide... let O be center of circle
<AOB = x1, <BOC = x2.. all angles in radians.. measured anticlock
required set := pi < x1 + x2 < 2pi, 2pi <x1 + x2 < 3pi
universe := 0 <=x1, x2 <= 2pi
so probability assuming uniform distribution = Area (pi < x1 + x2 < 2pi, 2pi <x1 + x2 < 3pi | 0 <=x1, x2 <= 2pi)/ Area (0 <=x1, x2 <= 2pi) = 3/4
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