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Magazine Problem 535
Show that the perimeter of an equilateral triangle which is inscribed in a circle with radius of length \(\mathrm{r}\) is \(3 \sqrt{3} \mathrm{r}\).
Problem 537
Show that for a triangle of area \(\mathrm{A}\), and perimeter \(\mathrm{P}\), the radius of the inscribed circle, \(\mathrm{r}\), equals \(2 \mathrm{~A} / \mathrm{P}\).
Problem 538
A regular hexagon is inscribed in a circle. If the length of the radius of the circle is 7 in. find the perimeter of the hexagon.
Problem 540
Find the perimeter of a regular polygon of n sides inscribed in a circle of radius \(\mathrm{r}=10\) when \(\mathrm{n}\) equals: a) \(3 ; \mathrm{b}\) ) \(4 ;\) c) \(6 ;\) d) \(9 ;\) e) \(12 ;\) f \(18 ; \mathrm{g}\) ) 36 h) Find the circumference of the circle using \(\pi=3.14\); i) Comparing the answers to parts (a) through (g) with the answer to (h), what conclusion do you reach?
Problem 542
Show that the perimeter of an n-sided polygon circumscribed about a circle whose radius has length \(\mathrm{r}\) is \(2 \mathrm{nr} \tan \pi / \mathrm{n}\).
