My Math Forum Distance between chords

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July 3rd, 2018, 09:21 AM   #1
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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?
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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: 12,211 Thanks: 521 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: $\displaystyle 2d=4\cos\left(\frac{\arccos\left(\frac{1}{7}\right )}{2}\right)=\frac{8}{\sqrt{7}}$ Thanks from MathsLearner123
July 3rd, 2018, 10:26 AM   #3
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Quote:
 Originally Posted by MathsLearner123 $\displaystyle \cos(\theta) =1/7=81.7.$
$\theta = \cos^{-1}\frac17= 81.8^\circ\!$ approximately.

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