Written by Sunny Yoon

This is a Geometer's Sketpad animation where a point P is animated about a polygonal path. An envelope of circles is traced where P is the center of each circle and each circle passes through a fixed point S. Explore. . .

This problem is presented in Dr. Wilson's homepage for EMAT 6690.

I decided to investigate polygonal path using different polygons or use a fixed point S as a center of a triangle and see how an envelope of circles is traced around the polygon.

After these two examples, I wanted to explore if there exists a difference between a convex/concave polygon.

 Convex Polygon Concave Polygon Pentagon Hexagon Heptagon Octagon

GSP file

Now, I decided to investigate regular polygon and using the center of the polygon as point S.

 Square Pentagon Hexagon Octogon

GSP file

Now, I'm going to investigate what happens when a polygon is a triangle and point S is the center of a triangle.

 Orthocenter Centroid Circumcenter Incenter

I used the same triangle when I was finding the center of the triangle.

What is the polygonal path when it is an obtuse triangle?

What is the polygonal path when it is a right triangle?