# 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
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 $\triangle ABC$, with common centroid $G$.

- 5 years, 2 months 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:

- 5 years, 2 months ago