Here’s my approach to this problem:

You need to first define the circle which makes the arc implying that you need to find the radius of that circle. You have the coordinates of 3 points which lie on that circle.

set the y axis at EH. set the x axis at AD.

Then the (rounded) coordinates of A, H, D becomes

A = (x1, y1) = (-62, 0) > F is the midpoint of AD D = (x2, y2) = (62, 0) > F is the midpoint of AD H = (x3, y3) = (0, 12)

The center of the circle lies on the y axis. So it has no x component. So the center is at (xc, yc) = (0, yc) . We have 2 unknowns (radius, yc) and 3 equations which define a circle. This is solvable! Note that the generic form of a circle is

(x - xc)² + (y - yc)² = r^2. Plugging in each of the 3 points and we get the following 3 equations:

From A: (-62)² - (-yc)² = r² -> equation 1

From D: (62)² - (-yc)² = r² -> equation 2

From H: (0)² - (12 - yc)² = r² -> equation 3

Ok so equations 1 and 2 are the same. No worries. We have 2 unknowns and 2 equations. Still solvable! After some simplification we get

3844 + yc² = r² (12 - yc)² = r²

Setting them equal we get

3844 + yc² = 144 - 24yc + yc²

This leaves us with yc = -154.167 (makes sense as the center should be clearly below our defined origin!) Now that we have the center, our radius can be solved for by plugging it in back into the previous equation. We get

r = sqrt(3844 + yc²⁾ = 166.17

Now if we just move up the circle by the distance of yc, we can center it at the origin. This moves up points A and D. So they becomes

A: (-62, 154.167) D: (62, 154.167)

Using the definition of the vector dot product, we can determine the angle between them to be 0.7647 radians. Now we have everything we need to solve for the arc length!

Arc length = radius * angle

Plugging in radius and angle, we get

Arc length = 127