2019 Nov P2 Q10.2

Question 10.2

$10.2$	In the diagram, $ST$ and $VT$ are tangents to the circle at $S$ and $V$ respectively. $R$ is a point on the circle and $W$ is a point on chord $RS$ such that $WT$ is parallel to $RV$ . $SV$ and $WT$ are drawn. $WT$ intersects $SV$ at $K$ . Let $\hat S_2=x$ .

$10.2.1$	Write down, with reasons, THREE other angles EACH equal to $x$ .	$(6)$
$10.2.2$	Prove, with reasons, that:
$\quad (a)$	$WSTV$ is a cyclic quadrilateral	$(2)$
$\quad (b)$	$\Delta WRV$ is isosceles	$(4)$
$\quad (c)$	$\Delta WRV\,\|\|\|\,\Delta TSV$	$(3)$
$\quad (d)$	$\frac{RV}{SR}=\frac{KV}{TS}$	$(4)$
		$\textbf{[19]}$