Description of Set

Here are a number of problems based around the same configuration: The solutions I have posted make use of areal/barycentric co-ordinates (two names for the same thing). These are useful in problems involving ratios of lengths, areas and cevians (lines from the verticies of a triangle to the sides that are concurrent at a point).

Full Description

Let OO be a point in acute-angle triangle ABCABC.

DD is the intersection of AOAO and BCBC. E,FE,F are defined similarly.

XX is the intersection of EFEF and ADAD. Y,ZY,Z are defined similarly.

Let PP be the intersection of XYXY and CFCF and QQ be the intersection of XZXZ and BEBE.

RR is the intersection of APAP with BCBC and SS is the intersection of AQAQ with BCBC.

Note by Sam Bealing
5 years, 2 months ago

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This looks nice!
Could you explain the configuration in detail, and the results you've obtained?
To me, it looks like the succesive medial triangles of ABC \triangle ABC , with common centroid G G .

Ameya Daigavane - 5 years, 2 months ago

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I've added a full description of the configuration. I've started to write the results I've derived as problems. Here are links to the first two:

Sam Bealing - 5 years, 2 months ago

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