Construct a pentagon/construction

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Given a circle, inscribe a regular pentagon.

Contents 1 Construction: Inscribed Pentagon 1.1 Step 0 1.2 Step 1 1.3 Step 2 1.4 Step 3 1.5 Step 4 1.6 Step 5 1.7 Step 6

[edit] Construction: Inscribed Pentagon

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

[edit] Step 0

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

[edit] Step 1

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

[edit] Step 2

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

[edit] Step 3

Draw a circle M with radius OM.

[edit] Step 4

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

[edit] Step 5

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

[edit] Step 6

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

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