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I was searching for a solution to a very practical problem asked by a friend of mine. The problem was that he had to lay a dropped kerb to allow vehicular access to customer's property... except the kerb was on a road bend. Since I am the closest person that he knows to qualify as a civil engineer, so he asked me to find a formula that could be used for this purpose. In the image is a diagram with workings to create the final formula for the unknown radius. My question is this: Is the formula and derivation universally correct? arc-chord length radial derivative formula

My result was $$r=\dfrac{4B^2+A^2}{8B}$$ Where B is the perpendicular height from midpoint of arc to midpoint of chord and A is the length of the chord itself.

I am concerned that I introduced an error in part 2 of the 3 steps of evaluation. Can anyone refute this?

Rhodie
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  • Maybe but my question is whether my answer I have formulated is correct. Since there is nobody available to help me locally I decided to ask the community. – Rhodie Sep 02 '18 at 02:29
  • Compare yours to the many solutions in the duplicate question. – amd Sep 02 '18 at 04:23

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I can't read your photo, but by the title you have a circular segment. The Wikipedia article has $$R=\frac {c^2}{8h}+\frac h2$$

Ross Millikan
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  • That doesn't look anything like what I have – Rhodie Sep 02 '18 at 02:35
  • $c$ is the distance between the endpoints of the arc and $h$ is the distance from the perpendicular height. – Ross Millikan Sep 02 '18 at 02:40
  • c is the chord length (your A) and h is the arc segment height (your B). so in your variables, R=A^2/8B+B/2, and over your common denominator, R=(A^2+4B^2)/8B. So yes, your formula is correct. Nice work! – VoteCoffee Jan 19 '20 at 19:35