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July 3rd, 2018, 10:21 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 11:04 AM.
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July 3rd, 2018, 10:41 AM   #2
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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:

$\displaystyle 2d=4\cos\left(\frac{\arccos\left(\frac{1}{7}\right )}{2}\right)=\frac{8}{\sqrt{7}}$
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July 3rd, 2018, 11:26 AM   #3
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Quote:
Originally Posted by MathsLearner123 View Post
$\displaystyle
\cos(\theta) =1/7=81.7.
$
$\theta = \cos^{-1}\frac17= 81.8^\circ\!$ approximately.
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