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 Two Obtuse Angles (Posted on 2007-01-27)
Let AB and BC represent two adjacent sides of square ABCD. If P is a randomly selected point inside of the square, and segments PA, PB, and PC are drawn, what is the probability that angle APB and angle BPC are both obtuse?

 See The Solution Submitted by Dennis Rating: 3.6000 (5 votes)

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 Solution | Comment 1 of 4
`For angle APB to be obtuse, point P must liein the circle with diameter AB. For angle BPCto be obtuse, point P must lie in the circlewith diameter BC. For both angles to be obtuse,point P must lie in the intersection of the circles. If ABCD is a unit square, then the probability is just the area of the intersection.`
`   2[(1/4)pi(1/2)^2 - (1/2)(1/2)(1/2)]`
`   = (pi-2)/8 ~= 0.1427`

 Posted by Bractals on 2007-01-27 17:08:01

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