Saturday, April 25, 2020

Dynamic Geometry 1474: Butterfly Theorem, Circle, Chords, Midpoints, 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 1474: Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration, iPad.
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3 comments:

  1. c.t.e.o.April 26, 2020 at 5:47 AM

    Draw HP // CF. From congrunce of two tr GM = MH
    Full explanation will be in my sketch

    ReplyDelete
  2. Sumith PeirisApril 27, 2020 at 4:04 AM

    Draw perpendiculars OK,ON from O to CF,ED respectively

    Obviously K and N are the midpoints of CF and ED respectively

    Since Tr.s CFM and EDM are similar, CF/CM = ED/EM
    Hence CK/CM = EN/EM & since < KCM = < MEN, Tr.s CKM & ENM are similar and so
    < GKM = < MNE...….(1)

    Now OMGK and OMNH are both concyclic so
    < GKM = < GOM ….(2) and
    < HOM = < MNE .…(3)

    From (1), (2) & (3) we have < GOM = < HOM and hence GM = MH

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete

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