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
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?
3 answers
its wrong
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 :)