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To draw a tangent to a circle from a given point not on the circle. |
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To draw a tangent to a circle from a given point not on the circle. |
| Given: Circle O with point P outside the circle. |
| Required: To draw a tangent to circle O from point P. |
| Procedure: |
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Use the segment command under the construct menu and construct segment
PO. |
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Bisect segment PO. (help) or select segment PO and use the midpoint command
under the construct menu to find the midpoint. Label the midpoint C. |
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Use the segment command under the construct menu
and construct segment CO. |
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Use the circle by center + radius command under the construct menu and
construct a circle with center at C and radius congruent to segment CO. |
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Label the intersections of circle C with circle O,
A and B respectively. |
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Use the ray command under the construct menu to construct rays PA and PB. |
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PA and PB are the required tangents. |
| Proof: |
Construct segments AO and BO;  PAO
and PBO
are right s.
(s
inscribed in a semicircle are right s) |
 PA
and PB are tangent to circle O. (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, do you always have two tangents? Why do the tangents disappear if you pull P inside 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 circle from external point |
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