[/quote]
Two known points are insufficient to arrive at a single unique solution. The reason is that we could fit those two known points very close together as a very small portion of a large circle, or far apart on a smaller circle. In both cases, the circle passes through the two points, but the centers of those two circles are entirely different points on the grid.

We need more information to calculate a solution. Since you wish to solve for a radius (and therefore a center) a third point would be needed as one way to allow for a unique solution.[/quote]



can't you find the length of the straight line from x2 - y2 and just center off that?

that is how I would lay out your driveway or sidewalk, well, if I was gonna lay out a driveway or a sidewalk for ya. 6/8/10 a 90 from center line of the straight line and poof, you got a driveway! [/quote]
Yes, the midpoint of the chord can be located. (The chord is the straight line between two points on a circle. Then we could mark a radius, but we don't know how FAR it is to the center of the circle. When you layout some concrete forms, you are also "mentally" doing some curve fitting. You choose a radius that smooths the lines together, and that's by sight for aesthetics. He's working with a grid in a program, so that human choice can't be injected.[/quote]


now I got the confuzed, shot that driveway right in the asphalt!

On paper use a compass.

Point of compass on one end point of original arc, scribe another arc. Move compass to other end point, scribe another arc crossing first one.

Do the same for the opposite side of your original arc.

Draw a line between the intersection point of the four arcs you made (you will have two new arcs on each side of the original arc).

Where that line crosses the arc in question is the midpoint.

In the field I use string and spray paint.

Watch this and you might get a better understanding rather than deciphering what I wrote. Center of an Arc

dude, they're engineers, we lost them at driveway.

Hop I figured my simplistic real world example didn't impress anyone. My sons an engineer and I have to bring him back to earth every now and then.

I have one year of college. Fortunately I went to a really good HS. The air force taught me to strive and lead and it's served me well. That said, I won't hire an engineer with a GPA above 3.5. They're just weird.

I have this in my office. So, so true...

Never confuse education with intelligence!

from each end point of the arc draw a line to the center point. From the center point of each line you just drew come off with a line at 90 degrees where they intersect will be the center of the circle

Your solution assumes an arc already exists. You also assume that a midpoint on that arc is known. He actually doesn't have an arc. He has TWO and ONLY TWO points in 2D space. He WANTS an arc to connect them, but we know nothing about the size of the circle from which the two points he has provided are taken. He must give us THREE points in order to solve the problem. You have assumed an arc that doesn't exist, and a point on that arc that he doesn't have identified. While your solution is the same as my original one, it doesn't work, and actually nothing will because we need to know 3 points to solve it.

Correct.