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To draw a tangent to a circle through a given point on the circle. |
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To draw a tangent to a circle through a given point on the circle. |
| Given: Circle O and point P on the circle |
| Required: To draw a tangent to circle O at point P |
| Procedure: |
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Use the line command under the construct menu and
construct line OP. |
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Locate and label any point A not on line OP. |
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Use the segment command under the construct menu
and construct segment AP. |
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Use the circle by center + radius command under the construct menu and
construct a circle with A as center and radius congruent to segment AP. |
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Label the intersection of line OP with the circle
centered at A, C. |
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Use the ray command under the construct menu and construct ray CA. |
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Label the intersection of ray CA with the circle centered at A, B. |
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Use the line command under the construct menu and construct line PB. |
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Line PB is tangent to circle O at P. |
| Proof: |
PB 
PC (An inscribed angle in a semicircle is a right angle) |
 PB is
tangent to the circle at P. ( A line
to the radius at its extremity on the circle is tangent to the circle) |
| Sketch: On the sketch below move point P around the circle, does PB stay tangent in every case? What point do you need to drag in order to change the size of the original circle? |
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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. tangent to point on circle |
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