You draw a square. Then, you draw the largest possible circle, tangent to all four sides. If the lower left corner of the square is at (0,0), and the sides of the square are parallel to the coordinate axis, the point (2,1) is on the circle, within the square.

What is the radius of the circle?

I would desparately like to agree with Larry, in fact I had agreed with him that there were two circles.

That two circles may be defined by the criteria of the given point on the circle, the xy origin and a containing square would seem given.

Then I thought,
let point (x,y) be on a tangent that coincides with an arc.
Let the point (x-dx, y-dy) be a point on the arc.
As dx and dy decrease the point is always going to be 'within' the arc side of the tangent.

At the limit, when dx and dy equal zero, the point on the arc cannot be within the arc's side of the tangent but on it.

This reasoning satisfies me as to a unique value, but only just.

What say you Larry?

Posted by brianjn on 2006-11-26 06:51:44