document.write( "Question 1190673: I want to make an octagon with all sides equal and all I have is a inside diameter. How can I figure this? \n" ); document.write( "

Algebra.Com's Answer #822390 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            From the context, you want to construct a REGULAR octagon.\r
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\n" ); document.write( "\n" ); document.write( "            This polygon has a central angle of 45 degrees, which is exactly HALF of the right angle.\r
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\n" ); document.write( "\n" ); document.write( "            The geometric construction procedure is as follows:\r
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document.write( "(1)  If you have a diameter, you have a radius, too.\r\n" );
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document.write( "        (you find the radius by dividing the diameter in two equal part:\r\n" );
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document.write( "         - - - by bisecting the diameter.  There is a special standard geometric construction for it, using a compass and a straightedge).\r\n" );
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document.write( "(2)  Having the radius, you draw a circle of this radius.\r\n" );
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document.write( "(3)  Then you draw an arbitrary diameter through the center, using the straightedge.\r\n" );
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document.write( "(4)  Having the diameter drawn, you construct a perpendicular to it through the center, using the compass and the straightedge.\r\n" );
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document.write( "(5)  Having this right angle, you divide it in two halves using the compass and the straightedge.\r\n" );
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document.write( "     In other words, you bisect this right angle.  There is a special standard procedure for it,\r\n" );
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document.write( "     using the compass and the straightedge.\r\n" );
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document.write( "(6)  Doing in the same way, you divide all right angles in two halves, drawing their bisectors.\r\n" );
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document.write( "     Doing this way, you obtain 8 intersection points on the circle, that are vertices of your octagon.\r\n" );
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document.write( "     The final step is to connect the consecutive vertices to get your figure.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Below are the links to my lessons in this site, describing standard geometric constructions\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO bisect a segment using a compass and a ruler\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO bisect an angle using a compass and a ruler\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO construct a triangle using a compass and a ruler \r
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