Question

A chord with a length of `1` runs from `pi/12` to `pi/8` radians on a circle. What is the area of the circle?

Answer 1

Area `=183.609" "`square units

Explanation:

From the data, an isosceles triangle can be formed with sides `1`, `r`, and `r`. The central angle `theta=pi/8-pi/12=pi/24`.

We can split this isosceles triangle into 2 right triangles with hypotenuse `r` and acute angle `1/2 theta=pi/48` and opposite to this acute angle `1/2 theta=pi/48` is side with length `1/2`.

We can now solve for `r`

`csc (pi/48)=r/(1/2)`

`r=7.64489`

and

Area`=pir^2=pi(7.64489)^2=183.609`

God bless....I hope the explanation is useful.