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Internal Common Tangents Exercise

Internal Common Tangents Exercise
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2023-05-26 03:04
CircleGeometric Construction
In collections Foundations of Geometry - Constructions
This example demonstrates the internal common tangents of two circles. Key mathematical concepts include the properties of circles and the definition of tangents. Using GeoGebra commands such as Circle, Point, Line, Intersect, Segment, and Tangent, the construction of the internal common tangents of two circles is illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, 3) → c
  2. Circle(B, 4) → d
  3. Point(c) → C
  4. Point(d) → D
  5. Circle(C, Segment[D, B]) → e
  6. Line(A, C) → a
  7. Intersect(e, a) → E, F
  8. Segment(A, B) → b
  9. Segment(B, F) → f
  10. Line(C, f) → g
  11. Intersect(g, b) → G
  12. Tangent(G, d) → h, i

AI Drawing Prompt Reference

Draw two circles, one with radius 3 and another with radius 4. Connect the centers of the circles to draw a line. Find the intersection points of the circles. Then draw a circle centered at one intersection point with a radius equal to the length of the line. Draw a line connecting the center and the intersection point. Draw a line connecting the intersection point to another circle's intersection point. Finally, draw a line connecting the two intersection points and a line from the intersection point to a tangent of the other circle.
The prompt above was compiled from the original drawing commands and is for reference only.