Question 48
Let $\triangle ABC$ be given and let $AA_1$, $BB_1$ and $CC_1$ be the medians of the triangle, which intersect at the point $T$, and let $\overline{A_1T}=\overline{A_1B}$. On the extension of $CC_1$ we choose a point $C_2$ such that $\overline{C_1C_2}=\frac{CC_1}{3}$, and on the extension of $BB_1$ we choose a point $B_2$ such that $\overline{B_1B_2}=\frac{BB_1}{3}$. Prove that the quadrilateral $TB_2AC_2$ is a rectangle.
