Sunday, May 24, 2020

Dynamic Geometry 1481: Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Dynamic Geometry 1481: Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration, GeoGebra, iPad.

8 comments:

  1. Let PE = e, PF =f, PG = g and PH = h

    Now we can apply the Pitot Theorem 5 times to the 5 inscribed quadrilaterals

    AE + h = AH + e …..(1)
    EB + g = BG + e …..(2)
    CF + g = CG + f …..(3)
    FD + h = DH + f …..(4)
    AB + CD = BC + AD ….(5)

    (1) + (2) + (3) + (4) - (5) gives us the desired result

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. BG+GC+AH+HD=AE+EB+CF+FD
    subtitute
    BG+GC=EB+CF+2.PG-EP-PF
    AH+HD=AE+FD+2.PH-EP-PF

    ReplyDelete
  3. Heard that Peru virus cases are climbing. Hope and pray u are Ok Antonio.

    Peter - hope u are safe in California too

    Also other Gogeometers Stan from Sweden, Nilton Lapa from Brazil, Ajith, Pradyumna and Praveen from India, Apostolis from Greece

    ReplyDelete
    Replies
    1. Thank you Sumith,
      Take care and best wishes!
      Antonio

      Delete
    2. Thanks Sumith,
      I am doing fine. Take care!

      Regards
      Pradyumna

      Delete
    3. Good to hear Pradyumna. Take care too.

      Sumith
      Moratuwa
      Sri Lanka

      Delete
  4. Thank you Sumith for your prayer
    Peter Tran from California, USA

    ReplyDelete