Circle Theorem 5: Radius to a Tangent

Circle Theorem 5: Radius to a Tangent
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2012-07-14 21:54
① This example demonstrates the circle theorem that the radius drawn to the point of tangency is perpendicular to the tangent line. ② Core mathematical concepts include circles, tangents, radii, perpendicular relationships, and angle measurement. ③ Construction highlights: a Circle command creates circle c; Point commands define center A and tangency point B; Segment connects A and B to form radius a; Tangent draws the tangent line b at B; Angle measures the angle γ between the radius and the tangent; auxiliary objects such as point C and segment d are also used. ④ Suitable for middle‑school geometry lessons, high‑school review, and as a dynamic GeoGebra tutorial for beginners.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Point(c) → B
  3. Segment(A, B) → a
  4. Tangent(B, c) → b,
  5. Point(b) → C
  6. Segment(B, C) → d
  7. Angle(A, B, C) → γ

AI Drawing Prompt Reference

Draw a circle c with center A and radius 5, then take a point B on circle c as the point of tangency, connect A and B to form radius a, draw the tangent line b at point B, then take a point C on tangent line b, connect B and C to form segment d, and finally measure angle γ, which is the angle between radius a and tangent line b.
The prompt above was compiled from the original drawing commands and is for reference only.