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Circles tangent to a given line and passing through two points

Circles tangent to a given line and passing through two points
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2020-04-23 23:19
CircleCoordinate GeometryGeometric Construction
This example demonstrates how to construct circles tangent to a given line and passing through two specified points. Key math concepts include circle equations, tangent properties, midpoints, and angle bisectors. GeoGebra commands used are Line, Intersect, Circle, OrthogonalLine, Midpoint, and LineBisector. Suitable for high school students learning analytical geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A_1, B_1) → l
  2. Line(B, A) → a
  3. Intersect(l, a) → C
  4. Circle(C, A) → c
  5. OrthogonalLine(C, a) → b
  6. Intersect(c, b) → D_1, D
  7. Intersect(c, a, 2) → E
  8. Midpoint(B, E) → M
  9. Circle(M, E) → d
  10. Intersect(d, b) → F_1, F
  11. Circle(C, F) → e
  12. Intersect(e, l) → H, G
  13. Intersect(e, l, 1) → G'
  14. OrthogonalLine(G, l) → f
  15. LineBisector(B, A) → g
  16. Intersect(f, g) → O
  17. Circle(O, A) → h
  18. OrthogonalLine(H, l) → i
  19. Intersect(g, i) → O'
  20. Circle(O', H) → k