Question

A circle's center is at `(7 ,4 )` and it passes through `(8 ,2 )`. What is the length of an arc covering `( pi ) /6` radians on the circle?

Answer 1

`root2(5)pi/6`

Explanation:

The radius is `AP=root2((7-8)^2+(4-2)^2)=root2(5)`

As the by definition an angle in radiants is exactly the ratio between the arc and the radius of the circumference where that arc is determined by that angle itself, we `pi/6=`("circular arc")`/R`.
As a result the arc length is "circular arc"`=R*pi/6`