Circumscribed Circle & Right Triangle

Circumscribed Circle & Right Triangle
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2015-11-23 20:48
This example demonstrates how to construct the circumcircle of a right triangle and illustrates its geometric properties. Key math concepts include circumcircle, right triangle, circle center, perpendicular bisector theorem, and angle measurement. Construction involves commands like Polygon, Midpoint, OrthogonalLine, Intersect, Circle, Angle, and Point to create the triangle, find midpoints, draw perpendiculars, determine intersections, and measure angles. Suitable for middle school and above students to understand the relationship between circles and triangles and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(b) → E
  4. OrthogonalLine(E, b) → d
  5. OrthogonalLine(D, c) → e
  6. Intersect(d, e) → F
  7. Circle(F, B) → f
  8. Angle(A, C, B) → α
  9. Angle(B, A, C) → β
  10. Angle(C, B, A) → γ
  11. Circle(G, 4) → g
  12. Point(g) → H
  13. Point(g) → I
  14. Polygon(H, I, J) → poly2, j, h, i
  15. Angle(H, J, I) → δ