Analysis and Approaches for IBDP Maths Ebook 2 | Page 95

2. In the figure, OHS, RHP , ORQ and PSQ are straight lines. OP
� � p , OQ � � q ,
� � �
OR : RQ � 1:3 and RH: HP � 2:3. It is given that OS ��OP� �OQ
, where � , � � .
(a) Show that ���
� 1.
(b) Express OH � in terms of p and q .
[4]
[5]
(c)
(d)
Hence, express OS
� in terms of p and q .
Hence, show that RS and OP are not parallel.
3. In the figure, QHP is a straight line. R and S are two distinct points inside the triangle
OPQ . OP
� � p , OQ � � q , p � 8, q � 6 , pq � �24
and
�
1 5
OR � p�
q. 6 9
[4]
[3]
8
(a) Find ˆ POQ .
(b) Show that OR � PQ and PR � OQ .
It is also given that
�
39
� �
SH � and SH � � OR , 0��
� 1.
3
[3]
[8]
(c) Find the value of � .
[5]
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