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To circumscribe a circle about a given triangle. |
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To circumscribe a circle about a given triangle. |
Given:  ABC |
| Required: To circumscribe a
circle around ABC. |
| Procedure: |
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Construct the perpendicular bisectors of two sides of the
triangle. This can be accomplished by following the basic
perpendicular bisector construction; (help, midpoint) (help,  )
or by using the
tools in Sketchpad which follows: |
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Select segment AB. |
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Use the midpoint command under the construct menu
to place a midpoint on AB. Label it D. |
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Select the midpoint D and segment AB; use the perpendicular line command
under the construct menu and construct a perpendicular at D. |
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Select segment BC and repeat the above steps, but
label the midpoint E. |
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Label the point of intersection of the two perpendicular bisectors point F. |
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Use the segment command under the construct menu and construct segment
FB. |
Use the circle by center + radius command under the
construct menu and construct a circle with center F and radius
congruent to segment FB. |
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This is the required circle. |
| Proof: |
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F is the intersection of the
bisectors. |
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Segment FB = FA = FC
(The
bisector of the sides of a triangle are concurrent in a point
equidistant from the vertices) |
ABC
is circumscribed by the circle. ( Definition of circumscribed) |
| Sketch: In the sketch below drag the vertices A, B, C around; does the circle still contain all 3 vertices? |
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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. circumscribe a circle around a triangle |
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