Three points are chosen at random on a circle of unit circumference. What is the probability that the triangle defined by these points as vertices has three acute angles? Hint: One of the angles is obtuse if and only if all three points lie in the same semicircle. Take the circumference as the interval [0, 1]. Take one point at 0 and the others at B and C.
Three points are chosen at random on a circle of unit circumference. What is the probability that the triangle defined by these points as vertices has three acute angles? Hint: One of the angles is obtuse if and only if all three points lie in the same semicircle. Take the circumference as the interval [0, 1]. Take one point at 0 and the others at B and C.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.4: Basic Constructions Justified
Problem 38E
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![16 Three points are chosen at random on a circle of unit circumference. What is
the probability that the triangle defined by these points as vertices has three
acute angles? Hint: One of the angles is obtuse if and only if all three points
lie in the same semicircle. Take the circumference as the interval [0, 1]. Take
one point at 0 and the others at B and C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2F4ef24f7b-01b9-4465-b740-0acf554e2bb7%2Fvrtszq8_processed.png&w=3840&q=75)
Transcribed Image Text:16 Three points are chosen at random on a circle of unit circumference. What is
the probability that the triangle defined by these points as vertices has three
acute angles? Hint: One of the angles is obtuse if and only if all three points
lie in the same semicircle. Take the circumference as the interval [0, 1]. Take
one point at 0 and the others at B and C.
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