## 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.

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

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

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

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

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

Regards