Question

If a chord is selected at random on a fixed circle, what is the probability that its length exceeds the radius of the circle?

Name: if a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle 13892
Uploaded: 2023-07-13T22:28:19-08:00
Duration: 3 min 31 s
Channel: Adi S
Description: if a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle 13892

          If a chord is selected at random on a fixed circle, what is the probability that its length exceeds the radius of the circle?

Added by Dustin C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/13/2023

Step 1

- A chord at distance m from the center has length L = 2 sqrt(R^2 - m^2). - L > R implies 2 sqrt(R^2 - m^2) > R ⇒ sqrt(R^2 - m^2) > R/2 ⇒ R^2 - m^2 > R^2/4 ⇒ m^2 < 3R^2/4 ⇒ m < (√3/2) R. -Equivalently, a chord is longer than the radius if its distance from the Show more…

Show all steps