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Explore Tangent-Chord Angles in Circles

Explore Tangent-Chord Angles in Circles
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2012-07-19 04:34
CircleAngleTrigonometryGeometric Construction
① This example demonstrates the tangent‑chord angle theorem: the angle between a tangent and a chord through the point of tangency equals the angle in the alternate segment. ② Core concepts: circle, tangent, chord, inscribed angle, tangent‑chord angle theorem. ③ Construction highlights: GeoGebra commands Circle, Point, Tangent, Segment, Angle, CircleArc; objects A, B, c, D, b, C, a, E, α, d, β, text1, text2. ④ Suitable for high‑school geometry instruction, student exploration, and classroom demonstration.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → D
  3. Tangent(D, c) → b,
  4. Point(c) → C
  5. Segment(C, D) → a
  6. Point(b) → E
  7. Angle(E, D, C) → α
  8. CircleArc(A, D, C) → d
  9. Angle(D, A, C) → β

AI Drawing Prompt Reference

Draw a circle with center A passing through B; pick a point D on the circle and construct the tangent at D; choose another point C on the circle and draw chord CD; select a point E on the tangent; mark the angle α between the tangent DE and chord CD, and the central angle β formed by radii AD and AC, also show the arc DC.
The prompt above was compiled from the original drawing commands and is for reference only.