user_rabbit_guide.txt

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RABBIT GENERATION - USER CONSTRUCTION GUIDE
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This guide provides examples of all available geometric constructions you can
input when DDAR reaches a fixed point and prompts for a construction.

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GENERAL FORMAT
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All constructions follow this pattern:
    constructor.construct_METHOD(Point1, Point2, ..., name_param='NewName')

- Points are referenced by their single-letter names (A, B, C, etc.)
- The name parameter varies by construction (see below)
- Some constructions have optional mark_points parameter (set to False by default)

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AVAILABLE CONSTRUCTIONS
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1. MIDPOINT (2 points)
   Constructs the midpoint of a segment.
   
   Syntax: constructor.construct_midpoint(A, B, name='M')
   
   Returns: Point M (midpoint of AB)
   Relations: midp M A B

   Example: constructor.construct_midpoint(A, B, name='M_AB')


2. ANGLE BISECTOR (3 points)
   Constructs the internal angle bisector of an angle.
   
   Syntax: constructor.construct_angle_bisector(A, B, C, pname='D')
   
   Points: A-B-C where B is the vertex
   Returns: Point D on segment AC
   Relations: col A C D, eqangle A B D D B C

   Example: constructor.construct_angle_bisector(A, B, C, pname='D')


3. EXTERNAL ANGLE BISECTOR (3 points)
   Constructs the external angle bisector of an angle.
   
   Syntax: constructor.construct_external_angle_bisector(A, B, C, pname='E')
   
   Points: A-B-C where B is the vertex
   Returns: Point E on line AC extended
   Relations: eqangle, eqratio, col A C E

   Example: constructor.construct_external_angle_bisector(A, B, C, pname='E_ext')


4. FOOT (PERPENDICULAR) (3 points)
   Constructs the foot of perpendicular from a point to a line.
   
   Syntax: constructor.construct_foot(P, A, B, name='H')
   
   Points: Drop perpendicular from P to line AB
   Returns: Point H (foot on line AB)
   Relations: perp P H A B, col A B H

   Example: constructor.construct_foot(P, A, B, name='H')


5. CIRCLE CENTER (3 points)
   Constructs the circumcenter of three points.
   
   Syntax: constructor.construct_circle(A, B, C, cname='O')
   
   Returns: Point O (center of circle through A, B, C)
   Relations: circle O A B C, cong O A O B, cong O A O C

   Example: constructor.construct_circle(A, B, C, cname='O')


6. INCENTER (3 points)
   Constructs the incenter of a triangle.
   
   Syntax: constructor.construct_incenter(A, B, C, name='I')
   
   Returns: Point I (incenter of triangle ABC)
   Relations: Angle bisector relations for all three angles

   Example: constructor.construct_incenter(A, B, C, name='I')


7. INCENTER2 (3 points)
   Constructs the incenter and incircle with tangency points.
   
   Syntax: constructor.construct_incenter2(A, B, C, name='I', mark_points=False)
   
   Returns: Points I, X, Y, Z (incenter and three tangency points)
   Relations: Incenter relations plus perpendicularity at tangency points

   Example: constructor.construct_incenter2(A, B, C, name='I')


8. EXCENTER (3 points)
   Constructs the excenter opposite to the first vertex.
   
   Syntax: constructor.construct_excenter(A, B, C, name='J')
   
   Returns: Point J (excenter opposite A)
   Relations: External angle bisector relations

   Example: constructor.construct_excenter(A, B, C, name='J')


9. EXCENTER2 (3 points)
   Constructs the excenter and excircle with tangency points.
   
   Syntax: constructor.construct_excenter2(A, B, C, name='J', mark_points=False)
   
   Returns: Points J, X, Y, Z (excenter and three tangency points)
   Relations: Excenter relations plus perpendicularity at tangency points

   Example: constructor.construct_excenter2(A, B, C, name='J')


10. CENTROID (3 points)
    Constructs the centroid of a triangle.
    
    Syntax: constructor.construct_centroid(A, B, C, name='G')
    
    Returns: Point G (centroid of triangle ABC)
    Relations: Medians and ratio relations (2:1 division)

    Example: constructor.construct_centroid(A, B, C, name='G')


11. ORTHOCENTER (3 points)
    Constructs the orthocenter of a triangle.
    
    Syntax: constructor.construct_orthocenter(A, B, C, name='H')
    
    Returns: Point H (orthocenter of triangle ABC)
    Relations: Altitude relations (perpendicularity)

    Example: constructor.construct_orthocenter(A, B, C, name='H')


12. ORTHOCENTER2 (3 points)
    Constructs the orthocenter with altitude feet.
    
    Syntax: constructor.construct_orthocenter2(A, B, C, name='H')
    
    Returns: Points H, D, E, F (orthocenter and three altitude feet)
    Relations: Orthocenter relations plus feet on sides

    Example: constructor.construct_orthocenter2(A, B, C, name='H')


13. MIRROR (2 points)
    Constructs the reflection of one point over another.
    
    Syntax: constructor.construct_mirror(A, B, name='A_prime', mark_points=False)
    
    Returns: Point A' (reflection of A over B)
    Relations: midp B A A', cong B A B A'

    Example: constructor.construct_mirror(A, B, name='A_prime')


14. ON DIAMETER (2 points)
    Constructs a point on a circle where AB is a diameter.
    
    Syntax: constructor.construct_on_dia(A, B, name='P')
    
    Returns: Point P such that angle APB = 90°
    Relations: perp A P P B

    Example: constructor.construct_on_dia(A, B, name='P')


15. INTERSECT LINES (4 points)
    Constructs the intersection of two lines.
    
    Syntax: constructor.construct_intersect_lines(A, B, C, D, name='P', mark_points=False)
    
    Points: Line AB intersects line CD
    Returns: Point P (intersection)
    Relations: col A B P, col C D P

    Example: constructor.construct_intersect_lines(A, B, C, D, name='P')


16. REFLECTION (3 points)
    Constructs the reflection of a point over a line.
    
    Syntax: constructor.construct_reflection(P, A, B, name1='P_prime')
    
    Points: Reflect P over line AB
    Returns: Points P' and H (reflection and foot)
    Relations: Reflection symmetry, perpendicularity

    Example: constructor.construct_reflection(P, A, B, name1='P_prime')


17. TANGENTS (3 points)
    Constructs tangent points from external point to a circle.
    
    Syntax: constructor.construct_tangents(P, O, Q, name1='T1')
    
    Points: From P to circle with center O passing through Q
    Returns: Points T1, T2 (two tangent points)
    Relations: Perpendicularity at tangent points, equal distances

    Example: constructor.construct_tangents(P, O, Q, name1='T1')


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TIPS FOR CHOOSING CONSTRUCTIONS
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1. Common triangle centers:
   - Incenter (I): Angle bisectors meet, useful for angle problems
   - Circumcenter (O): Perpendicular bisectors meet, useful for distance/circle problems
   - Centroid (G): Medians meet, useful for ratio problems
   - Orthocenter (H): Altitudes meet, useful for perpendicularity problems

2. For angle equality goals:
   - Try angle bisector constructions
   - Try similar triangle constructions (incenter, circumcenter)

3. For perpendicularity goals:
   - Try foot construction
   - Try orthocenter or altitude constructions
   - Try circle with diameter constructions

4. For distance/congruence goals:
   - Try midpoint construction
   - Try circle/circumcenter construction
   - Try reflection/mirror construction

5. For collinearity goals:
   - Try line intersection construction
   - Check if points lie on special lines (medians, altitudes, etc.)

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EXAMPLE WORKFLOW
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When DDAR reaches a fixed point, you'll see:

    Current problem state:
      Points: A, B, C, D
      Derived facts: 25
      Goals: 1
    
    Available points: A, B, C, D
    
    Example construction format:
      constructor.construct_midpoint(A, B, name='M_AB')
      ...
    
    Enter construction code (or press Enter to skip):
    >

At the prompt, type one of the constructions above. For example:

    > constructor.construct_foot(D, A, B, name='H')

This will construct the foot of the perpendicular from D to line AB, creating
point H and adding new geometric relations to help DDAR continue.

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NOTES
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- You can press Enter without typing to skip the construction and let DDAR fail
- Construction names should be unique and descriptive (e.g., 'M_AB' not just 'M')
- If a construction fails (e.g., points are collinear when they shouldn't be),
  DDAR will report an error and you can try again on the next rabbit call
- The mark_points parameter controls whether constructed points are drawn;
  it's usually set to False in rabbit mode to avoid cluttering the diagram

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