Geometry Problem. Post your solution in the comment box below.

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

Details: Click on the figure below.

## Thursday, August 9, 2018

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

Labels:
cevian,
excircle,
geometry problem,
isosceles,
parallel,
tangency point,
tangent,
triangle

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

ReplyDeleteExtend 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