Tuesday, July 17, 2018

Geometry Problem 1366: Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps.

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

Details: Click on the figure below.

Geometry Problem 1366: Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps..

Posted by Antonio Gutierrez at 12:34 PM
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4 comments:

  1. Sumith PeirisJuly 17, 2018 at 8:23 PM

    This follows very easily from my problem 1363 since < AHB = < ADB = 45

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. Peter TranJuly 17, 2018 at 10:18 PM

    https://photos.app.goo.gl/perU7VCwHMwg3bCF8

    Connect BD and draw altitude BK of triangle ABG
    Triangle BGF congruent to BCF ( case ASA)
    So BG=BC=BA
    In isosceles triangle ABG, AK is altitude and an angle bisector
    So ∠ (KBH)=1/2. ∠ (ABC)= 45 degrees => ∠ (BHK)= 45
    Since ∠ (BDA)= ∠ (BHA)= 45 => B, H, D, A are cocyclic with AD as a diameter
    So A,B,C,H,D are cocyclic

    ReplyDelete
  3. APOSTOLIS MANOLOUDISJuly 21, 2018 at 2:14 PM

    Is A,B,C,H,D=concyclic.

    ReplyDelete
  4. Antonio GutierrezJuly 22, 2018 at 8:20 PM

    test

    ReplyDelete

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