Final answer:
To find the probability that the 3 chosen points form a right triangle, we need to determine the total number of possible combinations of 3 points that can be chosen from the 8 equidistant points on the circle and the number of combinations that result in a right triangle. The probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Step-by-step explanation:
To find the probability that the 3 chosen points form a right triangle, we first need to determine the total number of possible combinations of 3 points that can be chosen from the 8 equidistant points on the circle. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Plugging in the values n = 8 and r = 3, we get:
C(8, 3) = 8! / (3!(8-3)!) = (8*7*6) / (3*2*1) = 56
Next, we need to determine the number of combinations that result in a right triangle. For a right triangle to be formed, the 3 chosen points must be at a distance of 90 degrees from each other.
There are 4 points on the circle that meet this criteria: The diameter (2 points), and the midpoints of the quarter arcs (2 points). Therefore, the number of combinations that result in a right triangle is 4.
Finally, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 56 = 0.0714