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To inscribe a regular hexagon in a circle. |
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To inscribe a regular hexagon in a circle. |
| Given: Circle with center O. |
| Required: To inscribe a hexagon in circle O. |
| Procedure: |
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 Label
any point on the circle point A. |
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Use the segment command under the construct menu and construct segment
OA. |
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Use the circle by center + radius command under the
construct menu and construct a circle with center A and radius congruent
to segment OA. |
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Moving counterclockwise around the original circle O, label the point of
intersection of these two circles B. |
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Repeat the above steps around the circle, until you
have 6 points labeled. |
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Use the segment command under the construct menu and construct segments
AB, BC, CD, DE, EF, and FA. |
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Hexagon ABCDEF is the required hexagon. |
| Proof: |
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OA = OB = AB ( radii of equal circles are equal) |
 OAB
is equilateral and
equiangular. (An equilateral
is equiangular) |
 AOB
= 60 ;
arc CD = 60
or 1/6 of a circle. (A central
measure = its intercepted arc and there are 360
in a circle.) |
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Chord AB is a side of a regular hexagon. Likewise for the rest of
the chords. ABCDEF is a regular hexagon. |
| Sketch: Before you try to move the points on the sketch below, can you predict which ones will move so that you can change the size of the hexagon? |
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This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use. inscribe a regular hexagon in a circle |
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