SOLUTION: If equilateral polygon PENTA is inscribed in a circle of radius 15 inches so that all of its vertices are on the circle, what is the length of the shorter arc from vertex P to vert

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Question 1070324: If equilateral polygon PENTA is inscribed in a circle of radius 15 inches so that all of its vertices are on the circle, what is the length of the shorter arc from vertex P to vertex N?
Answer by ikleyn(52864) About Me  (Show Source):
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If equilateral polygon PENTA is inscribed in a circle of radius 15 inches so that all of its vertices are on the circle,
what is the length of the shorter arc from vertex P to vertex N?
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1.  If equilateral polygon PENTA is inscribed in a circle, then the polygon is a REGULAR.


2.  The central angle of the polygon leaning to the shortest chord is  alpha = 2pi%2F5 = %28360%5Eo%29%2F5 = 72 degs.

    The central angle of the polygon leaning to the shorter arc from vertex P to vertex N is  beta = 2%2A%282pi%2F5%29 = 2%2A%28%28360%5Eo%29%2F5%29 = 144 degs.

    The length of the corresponding arc is  r%2Abeta = 15%2A2%2A%282pi%2F5%29 = 3pi = (3*2*2)*3.14 = 12*3.14 inches.


Calculate.

Solved.