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Ptolemy's Theorem Demonstration

Ptolemy's Theorem Demonstration
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2019-02-20 00:37
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates Ptolemy's theorem applied to cyclic quadrilaterals within a circle, dynamically proving the product relationship of the diagonals. It involves core mathematical concepts such as trigonometry, diagonal properties, and cyclic quadrilaterals. The construction uses GeoGebra commands like Circle and CurveCartesian, with objects including parameters b and α, points A, B, E_1, E_2, and lengths a, c, d, e. It is suitable for high school mathematics education to understand geometric properties of cyclic quadrilaterals and trigonometric applications.

GeoGebra Commands & Parameters

  1. Circle((0, 0), a) → c
  2. Circle(B, b) → d
  3. CurveCartesian((a * cos(t)) + (b * cos((5 * t))), (a * sin(t)) + (b * sin((5 * t))), t, 0, (2 * π)) → e

AI Drawing Prompt Reference

Draw a circle with radius a and another circle centered at point B with radius b, allowing them to intersect. Mark points E_1 and E_2 on the first circle, connect them, and draw a curve passing through E_1 and E_2 to illustrate diagonal relationships and trigonometric applications.
The prompt above was compiled from the original drawing commands and is for reference only.