Penciling

Lay out this plate in the same manner as the preceding plates.

Problem 13. How To Describe An Arc Or Circumference Through Three Given Points Not In The Same Straight Line

Locate the three points A, B, and C with a distance between A and B of about 2 inches and a distance between A and C of about 2 1/4 inches. Connect A and B and A and C. Erect perpendiculars to the middle points of A B and A C as explained in Problem 1. Now draw light pencil lines connecting the intersections I and J and E and F. These lines will intersect at 0.

With 0 as a center and a radius equal to the distance 0 A, describe the circumference passing through A, B, and C.

Proof

The point 0 is equally distant from A, B, and C, since it lies in the perpendiculars to the middle points of A B and A C. Hence the circumference will pass through A, B, and C.