A screenshot of the homework problem

$A$: The area of a circular segment with chord of length $b$, and height $h$.

$B$: The area of the isosceles triangle inscribed into the shape described in A.

Find of the limit of $A/B$ when the arc angle tends to $0$, then use that limit to approximate the area of a circular segment.

My main confusion with the question comes from the fact that to find the specified limit, I will need to use the formula for a circular segment, which is what im trying to prove in the first place.

  • 1
    $\begingroup$ You are asked to derive "approximate formula" which is probably limit times the area of the triangle. $\endgroup$
    – Vasili
    Mar 3 at 3:51
  • $\begingroup$ yes, but in evaluating the limit, you need to find the area of the segment, which is what you are trying to find in the first place. $\endgroup$
    – Fb_Wdw
    Mar 3 at 12:46

1 Answer 1


I've managed to figure it out. Thank you all! For those interested this is a picture of my work:


Essentially, you find the area of $A$ and $B$ in terms of the arc angle, then take the limit as the angle tends to $0$. Using the result, multiply it into the formula for $B$, thus approximating the area of $A$ in terms of only $b$, and $h$.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .