Construct a pentagon/construction

From OpenTutorial
Revision as of 07:11, 24 June 2006 by Bear (talk | contribs) (bring problem to sec 0)
Jump to navigation Jump to search

5star-04-finished.png

Given a circle, inscribe a regular pentagon.


Construction: Inscribed Pentagon

5star-05-given.png

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


Step 0

5star-06-step-00.png

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


Step 1

5star-07-step-01.png

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


Step 2

5star-08-step-02.png

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


Step 3

5star-09-step-03.png

Draw a circle M with radius OM.


Step 4

5star-10-step-04.png

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


Step 5

5star-11-step-05.png

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


Step 6

5star-12-step-06.png

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

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