2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle -Inscribed polygon An (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). b (b) (Approximate) Find an expression for the area An of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. (c) (Refine) Find the area of the circle by letting the number

2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle -Inscribed polygon An (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). b (b) (Approximate) Find an expression for the area An of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. (c) (Refine) Find the area of the circle by letting the number

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...

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2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C.
Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2
b
Circle
An
-Inscribed polygon
(a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0).
(b) (Approximate) Find an expression for the area A,, of the polygon (in terms of r and n only) by
adding the areas of all the triangles. Hint: There is not much to do here.
b
(c) (Refine) Find the area of the circle by letting the number
A = lim An
12-00

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