Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.

 May 3, 2023

P = 2/3


A circle is formed by every point in the plane that is a certain distance away from another point (center). Thus, it is a curve formed by points moving in the plane at a constant distance from a fixed point. It is also rotationallysymmetric about the center at all angles. A circle is a two-dimensional closed object in which every pair of points in the plane is equally spaced from the "center." A specular symmetry line is formed by a line that goes through the circle. It is also rotationally symmetric about the center at all angles.

We now want A and B to be separated by a distance greater than r. As a result, the angle should be greater than 60 degrees because the radius is equal to 60 degrees and decreases as the angle increases. As a result, point B cannot be in the 60-degree zone of A on both sides, that is, to A's left and right. 

As a result, probability = (angle where B can exist)/ (Total Angle)

P = (360 - (60)-(60))/360

P = 2/3

 May 4, 2023

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