MathPlotAI Logo MathPlotAI

Inscribed Rectangle in a Circle

Inscribed Rectangle in a Circle
Loading the math board and drawing, please wait…
2017-12-30 03:57
CirclePolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the construction of a rectangle inscribed within a circle, highlighting its geometric properties. Core math concepts include circle, rectangle, similarity transformation, linear functions, and equations. Key GeoGebra commands/objects used in the construction are Intersect, Circle, Point, Mirror, Polygon, Segment, Extremum, and Derivative. Suitable for high school mathematics education, exploring the relationship between circles and polygons, and the application of transformations.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → O
  2. Circle(O, r) → c
  3. Point(c) → A
  4. Mirror(A, yAxis) → B
  5. Mirror(A, xAxis) → D
  6. Mirror(D, yAxis) → C
  7. Polygon(A, B, C, D) → q1, a, b, c_1, d
  8. Intersect(d, xAxis) → H
  9. Intersect(a, yAxis) → I
  10. Segment(E, G) → g
  11. Segment(E, F) → h
  12. Extremum(f, 0, r) → Ext
  13. Polygon(I, O, H, A) → q2, i, o, h_1, a_1
  14. Derivative(f) → f'
  15. Intersect(f', xAxis, (3.5355339019578467, 6.359825910351447E-8)) → K
  16. Segment(Ext, K) → j