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Geometric Mean Construction

Geometric Mean Construction
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2019-08-10 03:07
CircleCoordinate GeometryGeometric Construction
This example demonstrates constructing a semicircle using the geometric mean of two points. The geometric mean of two positive numbers is their square root, and here, a semicircle c is constructed using the geometric mean of points A and B. Key construction commands include Point, Semicircle, Midpoint, and OrthogonalLine. Suitable for middle school and above students to learn about the concept and application of geometric mean.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Point(xAxis) → D
  5. Point(xAxis) → E
  6. Point(xAxis) → F
  7. Semicircle(A, F) → c
  8. Midpoint(A, F) → G
  9. Point(xAxis) → H
  10. OrthogonalLine(H, xAxis) → f
  11. Intersect(c, f, 1) → I

AI Drawing Prompt Reference

Draw points A and B on the x-axis, then construct a semicircle c with A and B as the endpoints of the diameter. Find the midpoint G of A and B, and then draw a perpendicular line f from another point H on the x-axis. The intersection I of the semicircle c and the perpendicular line f is the desired point.
The prompt above was compiled from the original drawing commands and is for reference only.