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Upon a given line segment as a chord, to describe an arc of a circle in which a given angle can inscribed. |
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Upon a given line segment as a chord, to describe an arc of a circle in which a given angle can inscribed. |
Given: Segment AB,
and  RST |
| Required: To
construct on AB as a chord a segment of a circle in which R
can be inscribed. |
| Procedure: |
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Label any point on ray SR P and any point on ray ST Q. |
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Use the segment command under the construct menu and construct segment
PQ. |
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With segment AB as a base line, construct DAB
= SPQ
and ABF
= PQT
(help) |
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Label the intersection of ray AD and ray BF point C. |
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Use the segment command under the construct menu
and construct segments AC and BC. |
Circumscribe a circle about  ABC.
(help) |
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Arc ACB is the required arc. |
| Proof: |
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ACB = RST
(If 2 s
of one
are = to 2 s
of another ,
the 3rd s
are =.) |
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Any
inscribed in arc ACB equals ACB.
(s
inscribed in the same arc are =.) |
| Sketch: |
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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. describe an arc into which an angle can be inscribed |
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