$P$, $Q$, $R$ and $S$ lie on a circle.
$PXR$ and $QXS$ are straight lines.
(a)[3]
Show that triangle $PQX$ is similar to triangle $SRX$.
Include a reason for every statement you make.
(b(i))[2]
With $PX = 8.1\,\text{cm}$, $QX = 6.3\,\text{cm}$ and $SX = 4.5\,\text{cm}$.
Work out $RX$.
(b(ii))[2]
Find the ratio
area of triangle $PQX$ : area of triangle $PSX$.
Give your answer in its simplest form.
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