July 3rd, 2018, 09:21 AM  #1 
Member Joined: Aug 2017 From: India Posts: 45 Thanks: 2  Distance between chords
My attempt: $\displaystyle \cos(\theta) =1/7=81.7. $ It is the same for both the angles. But how to find distance? Last edited by skipjack; July 3rd, 2018 at 10:04 AM. 
July 3rd, 2018, 09:41 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs 
As: $\displaystyle \arccos(x)= \text{arcsec}\left(\frac{1}{x}\right)$ where $\displaystyle x\ne0$ We see the two chords subtend the same angle, and are therefore the same distance $\displaystyle d$ from the center. Thus, the distance between the two chords is: $\displaystyle 2d=4\cos\left(\frac{\arccos\left(\frac{1}{7}\right )}{2}\right)=\frac{8}{\sqrt{7}}$ 
July 3rd, 2018, 10:26 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,502 Thanks: 1739  

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