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lvl10720-Turquoise
20-Turquoise
January 7, 2023
Solved

Butterfly Problem, solving with MathCad ?

  • January 7, 2023
  • 1 reply
  • 2636 views

    Hello Everyone.
   With referring to Werner's suggestion and Ttokoro's suggestion on solving with MathCad ( or Prime )

https://community.ptc.com/t5/Mathcad/Butterfly-problem/m-p/848009#M204472
I'm interesting in it :

Given:
Let ABC be a triangle with incircle ( O ), and let ( O ) touch BC, CA, AB at A', B', C' respectively. M is a
arbitrary-point move on B'C'. Lines BM and CA meet at B''. Lines CM and AB meet at C''. Lines A'M
and B''C'' meet at A''.
Prove :
A'' move on incircle ( O ) ( with M move on B'C'. )

Figure.PNG

     Thanks in advance for your time and help.
          Best Regards.

                 Loi.

 

Best answer by Werner_E

Here is a brute force attack with Mathcad.

Good luck for trying to let the symbolics prove it! 😈

But as you can see we can at least demonstrate the property for specific numeric values ...

Werner_E_0-1673174394422.png

 

 

Ani.gif

EDIT: modified screenshot and attached file! In the originals the radius was calculated wrongly

 

1 reply

W
Werner_E25-Diamond I
25-Diamond I
January 7, 2023

This characteristic property of a tangent quadrilateral should help:

https://www.cut-the-knot.org/Curriculum/Geometry/CircumQuadri.shtml

W
Werner_E25-Diamond IAnswer
25-Diamond I
January 8, 2023

Here is a brute force attack with Mathcad.

Good luck for trying to let the symbolics prove it! 😈

But as you can see we can at least demonstrate the property for specific numeric values ...

Werner_E_0-1673174394422.png

 

 

Ani.gif

EDIT: modified screenshot and attached file! In the originals the radius was calculated wrongly

 

    L
    lvl10720-TurquoiseAuthor
    20-Turquoise
    January 9, 2023

    Many, many thanks for your time and help, Werner.:

    1.png  2.png  3.png

    4.png

    5.png

    6.png

    7.png

    8.png

    9.png

    10.png

    11.PNG

    Best Regards.

       Loi.

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