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A door of width 6 meter has an arch above it having a height of 2 meter. Find the radius of the arch I analysed the problem to calculate the radius of curvature and I could not establish the relation between radius and height. Please someone help me to solve this using Pythagoras theorem on right angled triangle

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Hint: Draw a picturepicture
The radius of the arch is $r=2+h$

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  • $\begingroup$ How can I calculate the value of h $\endgroup$ – Achari S Ganesha Jul 8 '14 at 18:36
  • $\begingroup$ Is h=1.25cm and r=3.25cm $\endgroup$ – Achari S Ganesha Jul 8 '14 at 18:47
  • $\begingroup$ That is close. The units of the problem are meters, not centimeters. $\endgroup$ – Ross Millikan Jul 8 '14 at 19:45
  • $\begingroup$ If you extend the vertical line into a diameter, then you have $2 \times (2r-2) = 3 \times 3$ by power of a point. $\endgroup$ – Hao Ye Jul 9 '14 at 7:39
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$r=2+h$
Also, \begin{align*} r^2 & =h^2+3^2\\ (2+h)^2 & = h^2+3^2 \end{align*} Solving we get $h = 1.25~\text{m}$, so radius $=2+h=2+1.25= 3.25~\text{m}$

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    $\begingroup$ Here is a brief introduction to using $\LaTeX$ in your posts to create mathematical expressions. It has links to more extensive documentation, including the homegrown MathJax Basic Tutorial and Quick Reference. $\endgroup$ – hardmath Aug 24 '15 at 18:35
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If radius is R, use property of circle of constant segments length product.

$$ 2 ( 2 R -2) = 3*3 \rightarrow R = \frac{13}{4}= 3.25 $$

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