Using a ball, a sheet of paper, a compass, a straightedge without markings, and a pencil, can you draw a line segment on the paper equal to the ball's radius?
Step 1. Choose a point
on the ball and draw a circle with center
on the ball. Choose points
on that circle.
Step 2. Draw a triangle congruent to
on the paper and construct the center
of its circumscribed circle.
Step 3. Draw two mutually perpendicular lines (horizontal and vertical) through
be the intersection of the horizontal line with the circle. Find the point
on the vertical line such that the segments
are equal. (
is also equal to the segments
Step 4. Find the intersection
of the vertical line and the line perpendicular to
If the point
on the ball, then triangle
is congruent to
. So the segment
equals the diameter of the ball.
Step 5. To get a segment equal to the ball's radius, construct point
, the midpoint of segment