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Circle Tangent to Two Circles

Circle Tangent to Two Circles
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2015-08-04 20:10
CircleGeometric ConstructionLocus
This example demonstrates constructing a circle that is externally tangent to two given circles. Key mathematical concepts include circle properties and geometric construction. It uses commands such as Circle, Point, Line, Intersect, LineBisector, and Locus in GeoGebra. Suitable for middle school and above students to learn about circle properties and geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(C, D) → d
  3. Point(c) → E
  4. Line(A, E) → a
  5. Circle(E, Radius[d]) → e
  6. Intersect(e, a, 2) → F
  7. LineBisector(C, F) → b
  8. Intersect(a, b) → G
  9. Circle(G, E) → f
  10. Locus(G, E) → loc1

AI Drawing Prompt Reference

Draw two circles A and B, then construct a circle that is externally tangent to both. First, draw two circles with A and B as centers. Then, choose a point E on circle A and draw a line a through A and E. Next, draw a circle e with E as center and the radius of circle B. Find the second intersection point F of line a and circle e. Draw a line b through C and F, then find the intersection point G of line a and b. Finally, draw a circle f with G as center and E as radius, which is externally tangent to both circles A and B.
The prompt above was compiled from the original drawing commands and is for reference only.