25. From a point on the circumference of a circle of radius a, a chord is drawn in a random direction (all directions are equally likely). 4a and that the TC Show that the expected value of the length of the chord is variance of the length is 2a' (1 – 8/n). Also show that the chance is that the length of the chord will exceed the length of the side of an equilateral triangle inscribed in the circle. /

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CT: Test
Problem 14CT
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From a point on the circumference of a circle of radius a, a
chord is drawn in a random direction (all directions are equally likely).
25.
4a
and that the
Show that the expected value of the length of the chord is
variance of the length is 2a (1 – 8/n). Also show that the chance is that
the length of the chord will exceed the length of the side of an equilateral
triangle inscribed in the circle. /
Transcribed Image Text:From a point on the circumference of a circle of radius a, a chord is drawn in a random direction (all directions are equally likely). 25. 4a and that the Show that the expected value of the length of the chord is variance of the length is 2a (1 – 8/n). Also show that the chance is that the length of the chord will exceed the length of the side of an equilateral triangle inscribed in the circle. /
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