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..

4 comments:

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

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. 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