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Given a circle, inscribe a regular pentagon.


Contents

Construction: Inscribed Pentagon

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Although we generally consider the circle as given, in theory we should always start with two given (arbitrarily chosen) points.


Step 0

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Given points A and O, draw circle O with radius AO and diameter AA'. Let AO be 1 unit.


Step 1

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Construct the perpendicular bisector of AA' and find one intersection with circle O; call this S.


Step 2

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Construct the perpendicular bisector of SO and find its intersection with line SO; call this M.


Step 3

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Draw a circle M with radius OM.


Step 4

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Draw a line through A' and M. Find its intersections with circle M; call these P and Q.


Step 5

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Draw (two) circles with center A' and radii QA' and PA'. Find their intersections with circle O; call these B, C, D, and E.


Step 6

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Draw lines AB, BC, CD, DE, and EA.

I say the figure ABCDE is a regular pentagon. QEF.