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Radius Perpendicular Bisector of a Chord

Radius Perpendicular Bisector of a Chord
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2012-11-11 22:42
TriangleCircleAngleGeometric Construction
① This example demonstrates that the radius drawn to the midpoint of a chord is perpendicular to the chord and bisects it. ② Core mathematical concepts include circles, chords, radii, perpendicular bisectors, right angles, isosceles triangles, and chord‑center distance. ③ Construction highlights: GeoGebra commands Circle (create circle), Segment (draw chord), Point (mark endpoints and midpoint), OrthogonalLine (construct line through center perpendicular to chord), Intersect (find intersection), Angle (measure angle), Distance (compute segment lengths); objects used are A, B, c, a, C, b, D, E, α, distanceEC, TextEC, distanceCD, TextCD. ④ Suitable for high‑school geometry instruction, geometric construction practice, and independent exploration, serving as a classroom demo or homework resource.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → a
  3. Point(a) → C
  4. OrthogonalLine(C, a) → b
  5. Intersect(c, b, 2) → D
  6. Intersect(c, b, 1) → E
  7. Angle(A, C, D) → α
  8. Distance(E, C) → distanceEC
  9. Distance(C, D) → distanceCD

AI Drawing Prompt Reference

Draw a circle, pick two points on its circumference to form a chord, mark the chord’s midpoint, draw the line through the circle’s center perpendicular to the chord so it meets the circle at two points, creating two radii; indicate the angle between the center, the midpoint, and one intersection, and measure the distances from the midpoint to both intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.