Theorem-proof

Question 9.1

$9.1$	In the diagram, $O$ is the centre of the circle. Points $S$ , $T$ and $R$ lie on the circle. Chords $ST$ , $SR$ and $TR$ are drawn in the circle. $QS$ is a tangent to the circle at $S$ .

	Use the diagram to prove the theorem which states that $Q\hat ST=\hat R$ .	$\textbf{[5]}$

$10.1$	In the diagram, $\Delta ABC$ is drawn. $D$ is a point on $AB$ and $E$ is a point on $AC$ such that $DE\parallel BC$ . $BE$ and $DC$ are drawn.

	Use the diagram to prove the theorem which states that a line drawn parallel to one side of a triangle divides the other two sides proportionally, in other words prove that $\frac{AD}{DB}=\frac{AE}{EC}$	$\textbf{[6]}$