# 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 $$O$$ be a point in acute-angle triangle $$ABC$$.

$$D$$ is the intersection of $$AO$$ and $$BC$$. $$E,F$$ are defined similarly.

$$X$$ is the intersection of $$EF$$ and $$AD$$. $$Y,Z$$ are defined similarly.

Let $$P$$ be the intersection of $$XY$$ and $$CF$$ and $$Q$$ be the intersection of $$XZ$$ and $$BE$$.

$$R$$ is the intersection of $$AP$$ with $$BC$$ and $$S$$ is the intersection of $$AQ$$ with $$BC$$.

Note by Sam Bealing
2 years, 1 month 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 $$\triangle ABC$$, with common centroid $$G$$.

- 2 years, 1 month ago

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:

- 2 years, 1 month ago