MathPlotAI Logo MathPlotAI

Circle tangent to two given circles

Circle tangent to two given circles
Loading the math board and drawing, please wait…
2019-05-28 05:38
CircleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates how to construct a circle that is tangent to two given circles. The core mathematical concepts involved include circle, tangent line, coordinate geometry, and geometric construction. The construction utilizes GeoGebra commands such as Circle, Point, Line, Intersect, LineBisector, and Locus. It is suitable for high school students and teachers learning coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a circle tangent to two given circles by first creating the two circles, finding a point on one circle, connecting this point to the center of the first circle, drawing a circle with the center at this point and radius equal to the radius of the second circle, locating the two intersection points of this new circle with the previous line, then drawing the perpendicular bisector of the line segment connecting these points to the center of the second circle, finding the intersection of this bisector with the previous line, and finally drawing a circle with centers at this intersection point and the previously found point to get the tangent circle.
The prompt above was compiled from the original drawing commands and is for reference only.