Thursday, June 30, 2011

A Triangle Puzzle

three points are randomly chosen on a circle.what the probability that
1.triangle formed is right angled triangle.
2.triangle formed is acute angled triangle.
3.triangle formed is obtuse angled triangle.

Let the three vertices be A, B, C. We denote the angle at
center by the arcs AB, BC, CA by x, y, z.

x + y + z = 360.

Hence, the sample space can be represented by the region
surrounded by lines

x > 0,
y > 0 , and
x + y < 360. For the acute angled triangle ABC max(x, y, z) < 180, i.e., x < 180, y < 180, and x + y > 180

It can be easily seen that the three constraints form a
region which has exactly 1/4-th area of the original
sample space.

Solution Given abc

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