W. Courtney Trabue
EMT-725 Problem Solving
Dr. Jim Wilson (Spring 1997)


Part 1: Construct a Circle tangent to three points.

Construction: Choose any three points A,B,C and connect then to form a triangle. Construct the perpendicular bisectors of the sides and you will notice that they all intersect at the same point. This point is equadistant from all three vertices of the constructed triangle. So use the distance from this intersection to a vertex as the radius of a circle, and you have it.

Click here for a GSP script of the above construction.

Part 2: Construct a Circle tangent to two points and a line.

Construction: Pick any two points A,B and a line L. Draw a ray from A thur B intersecting Line L at L' and continuing. Using L' as the center of a circle and the Segment BL' as the radius, draw a circle. The circle intersects Line L in two palces, L1 and L2. Choose L2. You now have THREE points ( A, B, L1 ). Here, repeat the proceedure used in Part 1 above. The same proceedure could be used with point L1, and you would get a different circle. Much larger. In face, too large to fit on this screen !

The circle of Apollonius is depicted in green.


Part 3 - 10 of this Problem will be continued during the summer.

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