Expert: Abe Mantell - 9/13/2005

Question
I have the chord length (84) and the height of the sector (11) but need the radius. I believe the formula to be c=square root of 4h(2r-h). I lack, sadly, the algebraic finesse to pull this one off.  Any help would be great. I am attempting to replicate an arched doorway but one with a longer width(chord)and would like them to look similar as they are next to each other. Thanks.

Answer
Hello Jeff,

So, the formula is: c=sqrt[4h(2r-h)]
So we square both sides: c^2=4h(2r-h)
Distribute: c^2=8hr-4h^2
Then add 4h^2 to both sides: c^2+4h^2=8hr
Now divide by 8h: (c^2+4h^2)/(8h)=r...OK?

Now let c=84 and h=11...to get r=85.682

OK?

Abe