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.

3 comments:

  1. 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

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  2. 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

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  3. 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

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