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Inscribed Angle Theorem and Tangent‑Secant Corollary Demo

Inscribed Angle Theorem and Tangent‑Secant Corollary Demo
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2020-08-20 23:59
CircleAngleTransformationGeometric Construction
① This example demonstrates the inscribed angle theorem and the tangent‑secant corollary derived from it. ② Core mathematical concepts include inscribed angles, central angles, tangents, secants, chords, and angle bisectors. ③ Construction highlights: GeoGebra commands Circle, Rotate, CircleArc, Segment, Angle, Point, Line are used; objects such as center O, point A, circle p, angle α₁, point B, circle c, lines j and l, angle α, texts text1 and text2, segments a and b, point X, curve Curve, dependent Point, point C, functions f and g, and angle β appear. ④ Suitable for high‑school geometry instruction, geometric construction practice, and self‑study review of the inscribed angle theorem and tangent‑secant properties.

GeoGebra Commands & Parameters

  1. Circle(O, A) → p
  2. Rotate(A, α_1, O) → B
  3. CircleArc(O, A, B) → c
  4. Segment(O, A) → j
  5. Segment(B, O) → l
  6. Angle(A, O, B) → α
  7. Point(c) → X
  8. Point(p) → C
  9. Line(C, A) → f
  10. Line(C, B) → g
  11. Angle(A, C, B) → β

AI Drawing Prompt Reference

Draw a geometric figure with a center O and circle p, point A on the circle. Construct point B on the circle such that angle AOB equals α₁. Draw arc c from O to A and B, line segments j from O to A and l from B to O. Label angles α and β, showing relationships between circles, arcs, line segments, and angles. Suitable for geometry teaching and practice.
The prompt above was compiled from the original drawing commands and is for reference only.