Explorations in Geometry
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Construct a circle and create three new points on the circle (donít use the one that adjusts the radius). Create tangents to the three points and move them around the circle until they make a triangle on one side of the circle (see the figure). Now find the perimeter of the triangle.
1) Move the middle of the three points and the associated tangent and observe what happens to the perimeter of the triangle.
2) Now adjust the radius of the circle. What happens to the perimeter? 3) Make some other measurements on the figure and see if you can find a way to predict the perimeter as the circle is adjusted.
4) What would happen if the tangents were moved so that the circle was Inside the triangle formed? What discoveries about this shape can you make?
5) Write a brief paragraph and describe the relationships you have observed in this exploration.