Analysis and Approaches for IBDP Maths Ebook 2 | Page 165

Solution
11
(a)
(b)
(c)
OBA ˆ � ��
� A1
2
Similarly, OBC ˆ � ��
� .
2
ABC ˆ � �� � ��
� � M1
2 2
ABC ˆ �� � �
A1
ADC ˆ � � � ( � � �)
ADC ˆ � �
AG
BOD is a diameter if B , O and D are collinear. R1
AOD ˆ �� � �
Similarly, DOC ˆ �� � � . A1
The area of OCDA
1 1
� (1)(1)sin( � ��) � (1)(1)sin( � � �)
A1
2 2
1 1
� sin�
� sin�
2 2
� sin�
AG
(i)
�
� �
3
DOC ˆ
� �
� 2�
��
� �
3 3
ˆ 4�
DOC � � �
(A1) for correct value
3
1 1 �4�
�
A � (1)(1)sin � � (1)(1)sin � ���
(A1) for substitution
2 2 � 3 �
1 1 �4�
�
A � sin�
� sin � ���
2 2 � 3 �
A1
[3]
[3]
(ii)
dA
1 1 �4�
�
� cos�
� cos � ���( �1)
d�
2 2 � 3 �
dA
1 1 �4�
�
� cos�
� cos � ���
d�
2 2 � 3 �
dA
0
d� �
1 1 �4�
�
� cos�
� cos � ����
0
2 2 � 3 �
(A1) for correct approach
(M1) for setting equation
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