Saturday, October 1, 2016

Geometry Problem 1270 Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector

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 1270.

Geometry Problem 1270 Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector.

Posted by Antonio Gutierrez at 1:50 PM
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2 comments:

  1. Sumith PeirisOctober 1, 2016 at 6:54 PM

    < EAO = < EC1O = 90-A/2
    (since < C1CD = 90-C/2 and < C1DC = 90-B/2)

    Hence EAC1O is a cyclic quadrilateral

    So < AC1C = < AEO = 90

    Sumith Peiris
    Moratuwa
    Sri Lanka

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  2. Sumith PeirisOctober 2, 2016 at 5:43 AM

    Further if AO meets DE at A1 and CA1 and C1A meet at X then O,X,F are collinear points.

    Further if CX cuts FD at Z and AX cuts FE at Y then XF and YZ bisect each other. (XYFZ is a parallelogram)

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