construct triangle given angle and centroid

I am stumped by Euclidea problem 8.11:

From a triangle are given angle A and the centroid G

Construct the points B and C.

Please only a hint

1 Answer

HINT: We already know the position of angle $A$: position of $A$ and two rays $AB$ and $AC$, and the position of the centroid $G$. Taking the $A'$ in the ray $AG$ such that $A'G = 2 AG$, then from $A'$, draw two ray which respectively parallel with two ray of the angle $A$, and they cut the two ray of angle $A$ at $B$ and $C$. Prove that $G$ is centroid of a triangle $ABC$.