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Radius and Midpoint of Chord in a Circle

Radius and Midpoint of Chord in a Circle
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2015-06-26 10:53
CircleCoordinate GeometryGeometric Construction
In collections Circles Properties and Angle Properties of Circles
This applet demonstrates the relationship between the midpoint of a chord and the radius in a circle. Key mathematical concepts include circle properties, chord bisectors, and perpendicular chords. It uses GeoGebra commands such as Circle, Point, Segment, Midpoint, and OrthogonalLine for construction. Suitable for middle school and above students to learn geometric constructions and circle properties.

GeoGebra Commands & Parameters

  1. Circle(O, 5) → c
  2. Point(c) → A
  3. Point(c) → B
  4. Segment(A, B) → a
  5. Midpoint(A, B) → M
  6. Point(a) → N
  7. OrthogonalLine(N, a) → b
  8. Point(b) → C
  9. Point(b) → D
  10. Segment(C, D) → d
  11. Angle(C, N, A) → α
  12. Distance(N, B) → distanceNB
  13. Distance(N, A) → distanceNA

AI Drawing Prompt Reference

Draw a circle, pick two points on its circumference and join them to form a chord, mark the chord’s midpoint. Choose another point on the chord, draw the line through this point perpendicular to the chord; let this perpendicular intersect the circle at two points and connect them to form a segment. At the intersection of the perpendicular and the chord, measure the distances from this point to the chord’s endpoints and the angle formed by this point, one of the intersection points, and one endpoint of the chord.
The prompt above was compiled from the original drawing commands and is for reference only.