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Two Tangents Theorem

Two Tangents Theorem
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2012-07-10 16:39
CircleAngleGeometric Construction
This example demonstrates the geometric phenomenon that two tangents drawn from an external point to a circle are equal in length. Core math concepts include tangent lines, circles, line segment lengths, and angles. Construction highlights involve using GeoGebra commands such as Circle, Tangent, Intersect, and Distance to create the circle, tangents, intersection points, and measure segment lengths. Suitable for middle school and above students learning properties of circles and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(O, 5) → c
  2. Tangent(C, c) → a, b
  3. Intersect(c, b) → A
  4. Intersect(c, a) → B
  5. Distance(C, A) → distanceBC
  6. Distance(C, B) → distanceBD

AI Drawing Prompt Reference

Draw a circle with radius 5 centered at point O. From an external point C, construct two tangent lines to the circle, touching it at points A and B respectively. Connect point C to both tangent points, forming two line segments. Measure and label the lengths of these two segments, showing that they are equal. The diagram should clearly display the circle, the two tangents, the two tangent points, and the two segments from C to the tangent points, with their lengths indicated.
The prompt above was compiled from the original drawing commands and is for reference only.