Tuesday, July 5, 2016

Geometry Problem 1231: Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle

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 1231.


Geometry Problem 1231: Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle

3 comments:

  1. https://goo.gl/photos/eZPPUPkAJ3njjb2E7

    Draw OD ⊥ to AC ( D is on the circle O)
    D is the midpoint of arc AC
    since BI is the angle bisector of ∠(ABC) => B, I, D are collinear
    Triangle BOD is isoceles => ∠(OBI)=∠(ODI)
    but ∠(ODI)=∠(HBI) => ∠(HBI)=∠(OBI) => BI is the angle bisector of ∠( HBO)


    ReplyDelete
    Replies
    1. see correct link to this problem below:
      https://goo.gl/photos/NtEqqUcJsf3GfQgm6
      Peter Tran

      Delete
  2. Prøblem 1231

    < ABI = < CBI ......(1)
    < ABH = < CBO = 90-A ....(2)

    (1) - (2) gives the required result

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete