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Locus of a point subtending a right angle on two fixed points

Locus of a point subtending a right angle on two fixed points
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2017-12-18 14:21
CircleTrigonometryGeometric Construction
In collections Locus
This example demonstrates the locus of a point P moving such that it always subtends a right angle with two fixed points A and B, forming a right triangle. The locus is a circular arc. Key mathematical concepts include the definition of a circle, properties of right triangles, distance formulas in analytical geometry, and the geometric meaning of loci. The construction uses GeoGebra commands and objects like Angle, Segment, and If, as summarized, to dynamically show the path of P. It is suitable for high school students to learn about circle geometry and locus problems, serving as an example for analytical geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Angle(A, P, B) → α
  2. Segment(A, P) → a
  3. Segment(B, P) → b
  4. If(abs(Angle[A, P, B] - 90°) < 0.5°, P) → D
  5. If(Angle[A, P, B] > 90°, Angle[B, P, A]) → β
  6. If(abs(Angle[B, P, A] - 90°) < 0.5°, P) → E

AI Drawing Prompt Reference

Draw a figure showing the locus of a point P moving such that it always subtends a right angle with two fixed points, forming a circular arc. The path of P is dynamically shown, demonstrating properties of circles and right triangles, suitable for learning circle geometry and locus problems.
The prompt above was compiled from the original drawing commands and is for reference only.