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 $BC$ .

#Geometry

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 $G$ .

Ameya Daigavane - 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:

Sam Bealing - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$