The point P lies on the circle through the vertices of a rectangle QRST. The point X on the diagonal QS is such that $\overrightarrow {QX}$ = $2\overrightarrow {XS}$.
Express $\overrightarrow {PX}$, $\overrightarrow {QX}$ and ($\overrightarrow {RX}$ + $\overrightarrow {TX}$) in terms of $\overrightarrow {PQ}$ and $\overrightarrow {PS}$
I have calculated that $\overrightarrow {PX}$ = $\frac{1}{3}$$\overrightarrow {PQ}$ + $\frac{2}{3}$$\overrightarrow {PS}$
also that $\overrightarrow {QX}$ = $\frac{-2}{3}$$\overrightarrow {PQ}$ + $\frac{2}{3}$$\overrightarrow {PS}$ but I cannot do the last part.
$$\vec{RX}+\vec{TX}=\vec{RS}+\vec{SX}+\vec{TQ}+\vec{QX}=\vec{SX}+\vec{QX}=$$ $$=\frac{1}{3}\vec{SQ}+\frac{2}{3}\vec{QS}=\frac{1}{3}\vec{QS}=\frac{1}{3}(-\vec{PQ}+\vec{PS}).$$