Thursday, August 9, 2018

Geometry Problem 1376: Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines

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 1376: Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines.
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1 comment:

  1. UnknownSeptember 4, 2018 at 7:18 PM

    https://photos.app.goo.gl/51ioXWMypPWvkQf49

    Extend HG and FDB, intersect at I;

    Draw BU, GT as in the photo.

    Line BAP = BDF;
    So BP = BD+DF =BD+DX; (1)
    Line DBT=DCH
    DB+BT=DC+CH ;
    So DB+BY=DC+CH ;
    So DB= DC+CH-BY (2)
    From (1), (2);
    BP = BF= DX + DC+CH-BY =DX+DC-(BC-YC)+CH=XC-BC + 2CH= AX –AX+XC-BC+2CH
    =AC-AX- BC+2CH= AC-AX- BA+2CH =AC+2CH-BP
    So BP=1/2 AC+CH= BU
    BP=BF=BU;
    Because TGxBI = BUxGI;
    So GHXBI =BFxGI;
    So BI/BF = GI/GH
    So BG//FH


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