Oh c'mon folks, this isn't the Barrowman equations, do the math and keep your brain from turning into mush!

Circles are annoying, do triangles instead!

Example, a circles is such:

$$ r^2=(x-h)^2+(y-k)^2$$

Where [x,y] is the coordinates of your points on the circle and [h,k] are the coordinates of your center.

Since the radius is the same, you could write the circle equation for both points, set them equal to each other and solve for r and k (the radius, and the offset of the center)

If your center is at [0,0] then you end up with

$$x^2+y^2=r^2$$

which is suspiciously similar to the pythagorean theorem (triangle!)

You know 2 points [0,4] and [24,0] both of which are points along the circle that forms your ogive, and thus have the same radius.

Knowing that your circle center is at 0 on the x-axis simplifies things and allows us to skip the circle equation. As with any geometry problem, draw a picture first (exercise left to student)

Treating the cone axis as the x-axis, and cone base as the y-axis, we know your radius extends from circle center along the y-axis to your first point which is 4" above the x-axis [0,4]

If the first point [0,4] is above the x-axis, then your circle center will be below it and k is negative (sign convention is important!)

That means your radius is equal to 4 plus -k (the circle's y-offset)

$$(1): r=4+(-k)$$

If the 2nd point is on the x-axis (y=0) then we can draw a triangle with one leg equal to the center offset (-k) and the other leg equal to it's x position (24")

Applying pythagoras:

$$(2): r^2=24^2+(-k)^2$$

We once again have 2 equations with two variables: vertical circle offset (k) and circle radius (r) which you really want

Draw out -k from equation 1

$$(3): -k=r-4$$

Substitute in equation 2 so the whole thing is in terms of r

$$(4): r^2=24^2+(r-4)^2 $$

Solving for r

$$ 0=576+r^2-8r+16-r^2=>$$

$$8r=592=>$$

$$r=74$$

You have the number you want, but it's best for to finish the calc and check yourself. If the radius is 74 then the circle offset can be found

$$74=-k+4=>$$

$$k=-70$$

That result matches our earlier statement that k would be a negative value reflecting the circle's position below the x-axis

Final check

$$74^2=24^2+(-70)^2=>$$

$$5476=576+4900=>$$

$$5476=5476$$

And if you plug those values into the circle equation at the top for both your coordinates, it'll check out there too