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 5, 2023

After answering the question, we can state that probability in a circle = (angle where B can exist)/(Total Angle) => P = 2/3


What is a circle?

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 5, 2023

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