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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

Willemien
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  • Do we know the position of point $A$ (and the angle $A$) or we only know the angle $A$? How to determinate the position of point $G$ when we only know the angle $A$ (not position of this angle)? – GAVD May 12 '16 at 03:26
  • @GAVD Clearly $A$ is given, as well as the rays through $AB$ and $AC$. – Théophile May 12 '16 at 03:36
  • How is G 'given'? The distance from A? – N.S.JOHN May 12 '16 at 03:47

1 Answers1

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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 $ABC$.

GAVD
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