Let $T$ be a triangle, and $M$ its (first) Morley triangle:

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[![Morley](https://i.stack.imgur.com/BVj4Q.gif)](https://i.stack.imgur.com/BVj4Q.gif)

(Image from [Bruce Shawyer web page](http://www.math.mun.ca/~bshawyer/geom.html).)

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> ***Q1***. Does the centroid $c$ of $T$ ever fall outside of $M$?
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Let $m$ be the centroid of $M$.

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> ***Q2***. Among all triangles $T$ of unit area, which achieve the maximum
>  separation $\| c-m \|$ between the centroid of $T$ and the centroid of $M$?
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