Find the Points of Intersection of a Circle with a Line Segment

Geometric Construction with the Compass Alone

A circle is given by its radius R and the center O that lies on AB. Find the points of intersection of the circle with the segment AB.

Solution

From the point A swing an arc of arbitrary radius intersecting the given circle. Let C and D be the points of intersection. Using Problem #7 bisect two arcs CD of the original circle.


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