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

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

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## Monday, September 29, 2014

### Geometry Problem 1047: Parallelogram, Parallel Lines, Concurrent Lines, Diagonals

Labels:
concurrent,
diagonal,
Geometry,
parallel,
parallelogram,
Problem

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AG and HC meet at P, and HC and AB meet at Q. AQ=AH*CD/HD.

ReplyDeleteThen AP/PG=AQ/CG=(AH*CD/HD)/CG=(AH*CD)/(HD*CG).

AG and BO meet at P', and BO and CD meet at T. GT=(OG=HD)*(BE=CG)/(EO=AH)

Then AP'/P'G=(BA=CD)/GT=CD/(HD*CG/AH)=(AH*CD)/(HD*CG)

It has been shown that BO and HC meet at the same point of AG.