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OP in such a way that all points on OP have the same chance of being chosen. The chord passing through Q at right angles to OP meets the circle at points A and B. Find the probability density function of the length AB, and show that the probability that AB is greater than r is 0-866.

OP in such a way that all points on OP have the same chance of being chosen. The chord passing through Q at right angles to OP meets the circle at points A and B. Find the probability density function of the length AB, and show that the probability that AB is greater than r is 0-866.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In Figure 1.6, OP is a radius of a circle with centre O and radius r. A point Q is chosen on OP in such a way that all points on OP have the same chance of being chosen. The chord passing through Q at right angles to OP meets the circle at points A and B. Find the probability density function of the length AB, and show that the probability that AB is greater than r is 0-866. A Figure 1.6
Transcribed Image Text:In Figure 1.6, OP is a radius of a circle with centre O and radius r. A point Q is chosen on OP in such a way that all points on OP have the same chance of being chosen. The chord passing through Q at right angles to OP meets the circle at points A and B. Find the probability density function of the length AB, and show that the probability that AB is greater than r is 0-866. A Figure 1.6
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