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Equations of Circles (V3): Open Middle Problem

Equations of Circles (V3): Open Middle Problem
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2021-06-06 08:47
CircleCoordinate GeometryGeometric Construction
In collections Conic Sections Equations of Circles: 4 Open Middle Versions
This example demonstrates constructing the equation of a circle given certain conditions. Key mathematical concepts include the equation of a circle, coordinate geometry, and logic. GeoGebra commands such as Sequence, SelectedElement, Center, Point, Segment, Midpoint, Length, If, Polygon, Angle are used in the construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(i, i, -9, 9, 1) → hlist
  2. Sequence(i, i, 0, 9, 1) → tenslist
  3. Sequence(i, i, -9, 9, 1) → klist
  4. Sequence(i, i, -9, 9, 1) → xlist
  5. Sequence(i, i, -9, 9, 1) → ylist
  6. SelectedElement(hlist) → H
  7. SelectedElement(klist) → K
  8. SelectedElement(xlist) → xc
  9. SelectedElement(ylist) → yc
  10. SelectedElement(tenslist) → tensdigit
  11. Sequence(i, i, 1, 9, 1) → oneslist
  12. SelectedElement(oneslist) → onesdigit
  13. Center(eq1) → B
  14. Point(eq1) → C
  15. Segment(B, C) → f
  16. Midpoint(f) → D
  17. Length(Mode[l1]) → b
  18. If(b ≟ 0, "√", "×") → text5
  19. Polygon(B, E, A) → t1, a_1, b_1, e
  20. Segment(A, B) → g
  21. Segment(B, E) → h
  22. Segment(A, E) → i
  23. Angle(A, E, B) → α
  24. Midpoint(C, B) → F

AI Drawing Prompt Reference

On a coordinate plane, construct a circle whose center is point B and that passes through point C, reflecting the corresponding circle equation from given coordinate conditions. First define and select the coordinate-based points that determine B (the chosen center) and C (a point on the circle). Draw the segment BC, then take its relevant midpoint to set an auxiliary point F. Connect the key points to form a polygonal triangle-like shape, and include the segments that link the important vertices to show the geometric configuration. Mark the angle α formed by the two rays through the designated vertices, and display the associated length b with the appropriate nonzero indicator text.
The prompt above was compiled from the original drawing commands and is for reference only.