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Circle and Orthocenter Relationship Demo

Circle and Orthocenter Relationship Demo
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2016-12-23 04:13
CircleTrigonometryCoordinate GeometryGeometric Construction
In collections My 3D Collection
This example demonstrates the relationship between a circle, orthocenter, and unit circle through dynamic interaction, showcasing geometric properties. It involves core concepts like circle, orthocenter, unit circle, tree diagrams, and secant lines. Construction highlights include commands/objects like Surface, R, r, p, q, j, i, b, a, c, d, e, f, g, h from GeoGebra. Suitable for high school and above learners for understanding the integration of analytical geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Surface((2 * R) - i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (-2 * R) + r + i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → b
  2. Surface(((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), (-R) - r - j + (r * sin(u)^(1 / p)), u, 0, (2 * π), v, 0, (2 * π)) → a
  3. Surface((3 * R) - r - (2 * i) + (r * sin(u)^(1 / p)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → c
  4. Surface(((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), R + r + j + (r * sin(u)^(1 / p)), u, 0, (2 * π), v, 0, (2 * π)) → d
  5. Surface((2 * R) - i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (2 * R) - r - i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → e
  6. Surface((-2 * R) + i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (-2 * R) + r + i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → f
  7. Surface((-3 * R) + r + (2 * i) + (r * sin(u)^(1 / p)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → g
  8. Surface((-2 * R) + i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (2 * R) - r - i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → h