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The Wallace-Simson Line

The Wallace-Simson Line
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2015-02-15 02:32
CircleTrigonometryGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates that perpendiculars dropped from a point P on the circumcircle to the sides (extended) of a triangle are concurrent (their feet are collinear). Key concepts include circumcircle, perpendiculars, and collinearity. Constructed using commands like Line, Circle, Point, OrthogonalLine, Intersect. Suitable for high school and above, focusing on geometric properties and proofs.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. Circle(A, B, C) → d
  5. Point(d) → P
  6. OrthogonalLine(P, a) → e
  7. OrthogonalLine(P, c) → f
  8. OrthogonalLine(P, b) → g
  9. Intersect(a, e) → P_c
  10. Intersect(c, f) → P_b
  11. Intersect(b, g) → P_a
  12. Line(P_c, P_b) → h

AI Drawing Prompt Reference

Draw the circumcircle of triangle ABC, then select a point P on the circle. Construct perpendiculars from P to each side (extended) of the triangle, intersecting the sides at points P_a, P_b, and P_c. Finally, draw a line connecting P_a and P_b to form line h.
The prompt above was compiled from the original drawing commands and is for reference only.