Drawing triangle follow the picture: ![enter image description here]( $m$,$p$ and $Q$ are midpoints of segments we want to draw the triangle and we only have the lengh of $AM$,$BQ$ and $CP$ How to draw the triangle?

In the following mystic hexagon, the lengths of the dotted segments are $2m_a,2m_b,2m_c$ and the point $G$ is the centroid of the dotted triangle:

![enter image description here](

If the dotted triangle is given, we may construct the mystic hexagon by simply reflecting its centroid with respect to the midpoints of the triangle sides. That magic configuration serves also as a proof of:

> **Lemma 1.** If $a,b,c$ are the side lengths of a triangle, $m_a,m_b,m_c$ are the side lengths of a triangle.
>
> **Lemma 2.** If $a,b,c$ are the side lenghts of a triangle with area $\Delta$, the area of the triangle with side lengths $m_a,m_b,m_c$ is $\frac{3}{4}\Delta$.