Geometrical Constructions 2. - Workbook

István Makai, Feb 11, 2021

Table of Contents

  1. Radical axis, radical center
    1. W1/1 Radical center of three circles
    2. W1/2 Radical axis of two disjoint circles
    3. W2/1 Radical center of disjoint circles
  2. Apollonius' problem
    1. W2/2 Apollonius' problem PLL
    2. W3/1 Apollonius' problem LLL
    3. W4/2 Apollonius' problem PPL
    4. W5/1 Apollonius' problem PPC
  3. Ellipse
    1. W6/1 Basics of ellipse
    2. W7/2 Focus of an ellipse
    3. W8/1 Intersection of an ellipse and a line
    4. W8/2 Tangent of an ellipse parallel to a given direction
    5. W9/1 Tangents of an ellipse through an external point (special case)
    6. W9/1-2 Hyperosculating circles of an ellipse
    7. W9/2 Tangents to an ellipse through an external point
    8. W9/3 Rytz' construction
  4. Parabola
    1. W6/2 Basics of parabola
    2. W10/1 Construction of the directrix of a parabola
    3. W10/2 Construction of the focus and the directrix of a parabola
    4. W10/3 Intersection of a line and a parabola (special case 1)
    5. W10/4 Intersection of a line and a parabola (special case 2)
    6. W11/1 Tangent of a parabola parallel to a given direction
    7. W11/2 Intersection of a line and a parabola
    8. W11/2 Theory behind the construction of intersection points of a line and a parabola
  5. Hyperbola
    1. W7/1 Basics of hyperbola
    2. W7/3 Construction of the foci of a hyperbola
    3. W12/1 Construction of the vertices of a hyperbola
    4. W12/2 Construction of the asymptotes of a hyperbola
  6. Algebraic operations
    1. W12/3 Construction of √7
    2. W12/4 Construction of 1/√2

1.

Radical axis, radical center

  • 1. W1/1 Radical center of three circles
  • 2. W1/2 Radical axis of two disjoint circles
  • 3. W2/1 Radical center of disjoint circles

1.1.

W1/1 Radical center of three circles

– István Makai

1.2.

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1.3.

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2.

Apollonius' problem

  • 1. W2/2 Apollonius' problem PLL
  • 2. W3/1 Apollonius' problem LLL
  • 3. W4/2 Apollonius' problem PPL
  • 4. W5/1 Apollonius' problem PPC

2.1.

W2/2 Apollonius' problem PLL

– István Makai

2.2.

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2.3.

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2.4.

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3.

Ellipse

  • 1. W6/1 Basics of ellipse
  • 2. W7/2 Focus of an ellipse
  • 3. W8/1 Intersection of an ellipse and a line
  • 4. W8/2 Tangent of an ellipse parallel to a given direction
  • 5. W9/1 Tangents of an ellipse through an external point (special case)
  • 6. W9/1-2 Hyperosculating circles of an ellipse
  • 7. W9/2 Tangents to an ellipse through an external point
  • 8. W9/3 Rytz' construction

3.1.

W6/1 Basics of ellipse

– István Makai

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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4.

Parabola

  • 1. W6/2 Basics of parabola
  • 2. W10/1 Construction of the directrix of a parabola
  • 3. W10/2 Construction of the focus and the directrix of a parabola
  • 4. W10/3 Intersection of a line and a parabola (special case 1)
  • 5. W10/4 Intersection of a line and a parabola (special case 2)
  • 6. W11/1 Tangent of a parabola parallel to a given direction
  • 7. W11/2 Intersection of a line and a parabola
  • 8. W11/2 Theory behind the construction of intersection points of a line and a parabola

4.1.

W6/2 Basics of parabola

– István Makai

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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5.

Hyperbola

  • 1. W7/1 Basics of hyperbola
  • 2. W7/3 Construction of the foci of a hyperbola
  • 3. W12/1 Construction of the vertices of a hyperbola
  • 4. W12/2 Construction of the asymptotes of a hyperbola

5.1.

W7/1 Basics of hyperbola

Construction of the tangents at the vertices (perpendicular to the major axis) and the asymptotes are missing . Please see W12/2 how to construct the asymptotesin this case.
– István Makai

5.2.

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5.3.

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5.4.

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6.

Algebraic operations

  • 1. W12/3 Construction of √7
  • 2. W12/4 Construction of 1/√2

6.1.

W12/3 Construction of √7

– István Makai

6.2.

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