Question 160
Consider a half-disc with diameter $AB$ and centre $O$ and let $X$ be a point in the interior of the half disc. Denote the centroid of $XOB$ by $G$ and the second intersection of the line $AX$ with the boundary of the half-disc by $Y$. Prove that $YG = GB$. (Jiří Blažek, Josef Tkadlec)