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Point P on Line Segment

Point P on Line Segment
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2019-03-12 03:39
CirclePolygonGeometric Construction
This example demonstrates finding a point P on a line segment AB such that the length of AP forms the perimeter of a square and the length of PB forms the circumference of a circle. By adjusting the length of line segment AB, one can explore the position of point P under different conditions. Key mathematical concepts include geometric construction, properties of circles and squares. GeoGebra commands used include segment, midpoint, polygon, circle, intersection, area, etc. Suitable for middle school and above students to learn about geometry and the concept of pi.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. Midpoint(A, P) → C
  3. Midpoint(A, C) → D
  4. Midpoint(C, P) → E
  5. Polygon(P, E, 4) → poly1, n, p, q, r, F, G
  6. Circle(P + ((cos(π / 3) * (40 - a) / ((2 * π))), (sin(π / 3) * (40 - a) / ((2 * π)))), P) → f
  7. Line(B, H) → g
  8. Intersect(f, g, 2) → I
  9. Midpoint(P, B) → J
  10. Segment(A, P) → h
  11. Segment(P, B) → i
  12. Area(f) → j
  13. PointIn(f) → Pointf
  14. Segment(K, L) → l
  15. Midpoint(K, L) → M