limit of the area of a circular segment to the area of the inscribed isosceles triangle as the arc angle tends to $0$.

Question

$A$: 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.

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 $h$.