Thursday, June 16, 2011

Problem 624: Triangle, Incenter, Excenter, Incircle, Excircle, Similarity

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 624.

Online Geometry Problem 624: Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Posted by Antonio Gutierrez at 7:07 PM
Labels: , , , , ,

3 comments:

  1. PravinJune 16, 2011 at 8:13 PM

    ∠EAC = ∠BAI (∵ each = A/2)
    ∠AEC
    =∠IEC
    =∠IBC (∵B,I,C,E are concyclic)
    =B/2
    =∠ABI
    Hence ∆AIB ~ ∆ACE

    ReplyDelete
  2. Sumith PeirisNovember 29, 2015 at 9:29 AM

    If AC meets the excircle at X < ECX = 1/2 BCX = A/2 + B/2. So < AEC = < B/2

    So Tr. s ABI and AEC both have angles < A/2 and B/2 and are therefore similar

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. Sumith PeirisApril 27, 2016 at 6:51 AM

    Or since IBEC is con cyclic the result is obvious

    ReplyDelete

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