Saturday, January 21, 2017

Geometry Problem 1309 Triangle, Circle, Inradius, Excircle, Tangent, Exradius, Measurement

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 1309 Triangle, Circle, Inradius, Excircle, Tangent, Exradius, Measurement.

Posted by Antonio Gutierrez at 11:30 AM
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4 comments:

  1. c.t.e.o.January 21, 2017 at 12:05 PM

    P, P' tg points ( on AC, BC). Join O2 to C
    From AD=AE, PC=P'C, we get PC=11
    Right tr O1PP'~tr O2CE => 6/11=7/x => x=77/6

    ReplyDelete
  2. Peter TranJanuary 21, 2017 at 5:35 PM

    https://goo.gl/photos/gUJk9ftBfbk8pmpQ9

    Define points I, F, G, H and M as per sketch
    We have CG=CE=BF= 7 and BG=CF=CH=11
    We also have IC⊥CM
    Triangle IHC simillar to CEM ( case AA)
    So IH/CH= CE/ME => 6/11=7/x
    So x= 77/6

    ReplyDelete
  3. Sumith PeirisJanuary 21, 2017 at 11:38 PM

    If U,V,W are the tangency points of BC, CA, AB respectively of the in circle,

    Then WD = VE = BC = 18.

    So easily VC = 11
    Hence from similar right triangles O1VC and O2CE

    6/11 = 7/x and so x = 77/6

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  4. HenkieApril 12, 2017 at 7:11 AM

    You can also calculate AC. Just for the fun.
    That gives AC = 1099/41

    ReplyDelete

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