Tuesday, August 2, 2016

Geometry Problem 1242: Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to view more details of problem 1242.


Geometry Problem 1242: Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps

1 comment:

  1. Let BC and AD extended meet at P

    Then C2 is the excentre of Tr. PCD
    C1 is the in Centre of Tr. PCD
    A2 is the in Centre of Tr. PAB
    A1 is the excentre of Tr. PAB

    It follows that PC1C2A2A1 are collinear points, being on the internal bisector of < P. The concurrency of BC,AD and this line is also self evident

    Similarly for AB and DC extended which when extended say meets at Q. Then Q and B1,B2,D1,D2 are collinear and the concurrency of this line and AB and DC is evident

    Sumith Peiris
    Moratuwa
    Sri Lanka

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