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, November 17, 2019
Dynamic Geometry Problem 1447: Outer Vecten Point
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https://photos.app.goo.gl/LavifjVpqeaMipcLA
ReplyDeleteLet S is the midpoint of AB
Connect BF, AI, SO and SQ
Triangle ACI congruent to FCB ( case SAS)
ACI is the rotational image of FCB around C so AI= FB and AI ⊥FB
S, O and Q are the midpoints of AB, AF and BI => SO= SQ and SO ⊥SQ
Triangle SPO congruent to SAQ ( case SAS)
SAQ is the rotational image of SPO around S , 90 degrees
So PO=AQ and PO ⊥AQ
Similarly OQ=CP and OQ ⊥ CP and PQ = BO and BO⊥ PQ
In triangle OPQ, 3 altitudes QA, PC and OB will concur at orthocenter V
The concurrency part is trivial by Jacobi, and the rest part can be done by Baudhiyana's Theorem.
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