Sunday, November 17, 2019

Dynamic Geometry Problem 1447: Outer Vecten Point

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 Problem 1447: Outer Vecten Point. Using GeoGebra.

2 comments:

  1. https://photos.app.goo.gl/LavifjVpqeaMipcLA

    Let 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

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  2. The concurrency part is trivial by Jacobi, and the rest part can be done by Baudhiyana's Theorem.

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