Home Tutors Exams

Similarity-and-proportionality

Written on
November 2020 - Paper 2

Question 8.2

$8.2$	In $\Delta ABC$ , $F$ and $G$ are points on sides $AB$ and $AC$ respectively. $D$ is a point on $GC$ such that $\hat D_1=\hat B$ .

$\quad 8.2.1$	If $AF$ is a tangent to the circle passing through points $F$ , $G$ and $D$ , then prove, giving reasons, that $FG\parallel BC$ .	$(4)$
$\quad 8.2.2$	If it is further given that $\frac{\displaystyle AF}{\displaystyle FB}=\frac{\displaystyle 2}{\displaystyle 5}$ , $AC=2x-6$ and $GC=x+9$ , then calculate the value of $x$ .	$(4)$
		$\textbf{[8]}$

Written on
November 2019 - Paper 2

Question 8.2

$8.2$	In the diagram, the diagonals of quadrilateral $CDEF$ intersect at $T$ . $EF=9$ units, $DC=18$ units, $ET=7$ units, $TC=10$ units, $FT=5$ units and $TD=14$ units.

Prove, with reasons, that:
$\quad 8.2.1$	$E\hat FD=E\hat CD$	$(4)$
$\quad 8.2.2$	$D\hat FC=D\hat EC$	$(3)$
		$\textbf{[7]}$

Written on
November 2020 - Paper 2

Question 9.2

$9.2$	Chord $QN$ bisects $M\hat NP$ and intersects chord $MP$ at $S$ . The tangent at $P$ meets $MN$ produced at $R$ such that $QN\parallel PR$ . Let $\hat P_1=x$ .

$\:\: 9.2.1$	Determine the following angles in terms of $x$ . Give reasons
$\quad (a)$	$\hat N_2$	$(2)$
$\quad (b)$	$\hat Q_2$	$(2)$
$\:\: 9.2.2$	Prove, giving reasons, that $\frac{\displaystyle MN}{\displaystyle NR}=\frac{\displaystyle MS}{\displaystyle SQ}$	$(6)$
		$\textbf{[10]}$

Written on
November 2020 - Paper 2

Question 10

In the diagram, a circle passes through $D$ , $B$ and $E$ . Diameter $ED$ of the circle is produced to $C$ and $AC$ is a tangent to the circle at $B$ . $M$ is a point on $DE$ such that $AM\perp DE$ . $AM$ and chord $BE$ intersect at $F$ .

$10.1$	Prove, giving reasons, that:
$\quad 10.1.1$	$FBDM$ is a cyclic quadrilateral	$(3)$
$\quad 10.1.2$	$\hat B_3=\hat F_1$	$(4)$
$\quad 10.1.3$	$\Delta CDB\,\|\|\|\,\Delta CBE$	$(3)$
$10.2$	If it is further given that $CD=2$ units and $DE=6$ units, calculate the length of:
$10.2.1$	$BC$	$(3)$
$10.2.2$	$DB$	$(4)$
		$\textbf{[17]}$

Written on
November 2019 - Paper 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	$(4)$
$\quad (c)$	$\Delta WRV\,\|\|\|\,\Delta TSV$	$(3)$
$\quad (d)$	$\frac{RV}{SR}=\frac{KV}{TS}$	$(4)$
		$\textbf{[19]}$

← Back to the exams