Asked by anonymous
Three points are chosen uniformly at random from the perimeter of circle. The probability that the triangle formed by these is acute can be expressed as ab where a and b are coprime positive integers. What is the value of a+b?
Answers
Answered by
Steve
Place point A anywhere on the circle.
Draw a diameter from point A.
Now place point B. It lies on one side of that diameter.
There is a 50% chance that point C lies on the same side of the diameter as point B.
Now, if C is at the end of the diameter, ABC is a right triangle.
ABC is acute if C lies on the opposite side of the diameter from B.
The chance of that is 1/2, so a+b=3
Draw a diameter from point A.
Now place point B. It lies on one side of that diameter.
There is a 50% chance that point C lies on the same side of the diameter as point B.
Now, if C is at the end of the diameter, ABC is a right triangle.
ABC is acute if C lies on the opposite side of the diameter from B.
The chance of that is 1/2, so a+b=3
Answered by
Mathslover
its wrong
Answered by
saurav
its five...
let the points be abc,
put "a" anywhere. you can place b at diametrically opposite or not (1/2) then if they are not diametrical opposite then there are two sides where we can place c.and one gives acute and other gives obtuse... so 1/2
so 1/2*1/2=1/4 so 5..:P :)
let the points be abc,
put "a" anywhere. you can place b at diametrically opposite or not (1/2) then if they are not diametrical opposite then there are two sides where we can place c.and one gives acute and other gives obtuse... so 1/2
so 1/2*1/2=1/4 so 5..:P :)
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