Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Sunday, May 24, 2020
Dynamic Geometry 1481: Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration
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Let PE = e, PF =f, PG = g and PH = h
ReplyDeleteNow 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
BG+GC+AH+HD=AE+EB+CF+FD
ReplyDeletesubtitute
BG+GC=EB+CF+2.PG-EP-PF
AH+HD=AE+FD+2.PH-EP-PF
Heard that Peru virus cases are climbing. Hope and pray u are Ok Antonio.
ReplyDeletePeter - 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
Thank you Sumith,
DeleteTake care and best wishes!
Antonio
Thanks Sumith,
DeleteI am doing fine. Take care!
Regards
Pradyumna
Good to hear Pradyumna. Take care too.
DeleteSumith
Moratuwa
Sri Lanka
Thank you Sumith for your prayer
ReplyDeletePeter Tran from California, USA
U are welcome Peter.
Delete