Tool(s) Geometers Sketchpad

Data File(s) si2

Focus Tangents drawn at the vertices of an inscribed convex polygon and the angles they form exterior to the polygon and interior to the circle.

Tasks

1. After highlighting the angle measurements, use the Calculate option under the Measure menu to sum the angles. State a conjecture concerning the sum of the angles exterior to the inscribed polygon and interior to the circle. To prove your conjecture false, what sort of counter example would be necessary?

2. Construct the polygon interior and measure its area and perimeter. Do either of these quantities remain constant when a vertex is moved?

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