5.9: Convexity
- Page ID
- 23460
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5.9. Convexity
This short section presents a simple result which to some extent justifies the assumptions made in the previous section - namely that the perimeter (or area) of a regular n-gon inscribed in a circle is less than the perimeter (or area) of the circle, and of the circumscribed regular n-gon.
Problem 212 A convex polygon P1 is drawn in the interior of another convex polygon P2.
(a) Explain why the area of P1 must be less than the area of P2.
(b) Prove that the perimeter of P1 must be less than the perimeter of P2.