Draw a unit circle on a sheet of graph paper with lines spaced 1 unit such that one square is completely inside the circle.

The lines of the paper will intersect the circle in 8 places, cutting the circle into 8 arcs. Consider the 4 arcs where some of the grid lines cut the circle as shown in the diagram: AB, BC, CD, DA.

Describe, as precisely as possible, how to place the circle so the relative lengths of these arcs are in the extended ratio 1:2:4:3 in order around the circle. Use the coordinate system as in the diagram.

(In reply to Not obvious to me by Steve Herman)

Steve,
This problem is a modification of a problem that is yet to follow.  I misunderstood what that problem was about.  My proposal to Jer at that time was a challenge to his difficulty level.

You would be surprised just how close you are to locating the exact location of that centre.   You really only need some basic mid-high school geometry and trigonometry.

Posted by brianjn on 2013-05-24 23:21:02