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To inscribe a square in a given circle. |
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To inscribe a square in a given circle. |
| Given: Circle with center O. |
| Required: To inscribe a square in circle O. |
| Procedure: |
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Label any point on the circle A. |
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Use the line command under the construct menu and construct line AO. |
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Label the second intersection of line AO with the
circle point C. |
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Use the segment command under the construct menu and construct segment
AC. |
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Use the hide command under the display menu to hide
line AO. |
Construct a 
to AC through point O. (help) or use Sketchpad commands: |
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Select point O and segment AC; use perpendicular
line command under the construct menu and construct a perpendicular at
O. |
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Label the intersections of the perpendicular with
the circle points D and B. |
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Use the segment command under the construct menu and construct segment
DB. |
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Use the hide command under the construct menu to hide the perpendicular
line. |
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Use the segment command under the construct menu and construct segments
AB, BC, CD, and DA. |
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ABCD is the required square. |
| Proof: |
 A = B
= C = D
= 90 .
(An
inscribed in a semicircle is a right ) |
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arc AB = arc BC = arc CD = arc DA Equal
central angles intercept equal arcs. |
AB = BC = CD = DA (Equal arcs are subtended by equal chords) |
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ABCD is a square. (Sides are equal and s
are right s.) |
| Sketch: On the sketch below, why can't you drag all the points of the square? |
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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 square in a circle |
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