John E.

asked • 07/30/18

follow up question

Thanks Philip for the excellent answer. The follow up question is this. If you divide a circle of 880 by 5 the result is 5 equal arcs of 176. Why can't you fit a five pointed pentagon with 5 sides of 176 into it. Isn't five arcs of 176 equal to five sides of 176? If you draw lines and join the 5 arcs don't you have a pentagon? Is the length of an arc (176) equal to the side (176) of a pentagon? The five arcs of a circle and the five sides of the pentagon have the exact same perimeter. What is the largest pentagon that fits into a circle of 880. Please clarify. Thanks.

Philip P.

Take one of those arcs of 176 units.  Draw points at the start and end of the arc.  Now draw a straight line connecting the two endpoints you just drew.  That line is SHORTER than the 176 unit arc.  Hence the sides of the pentagon (which connect the endpoints of the five arcs) need to be shorter than 176 units.
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07/30/18

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