Analysis and Approaches for IBDP Maths Ebook 2 | Page 164

Your Practice Set – Analysis and Approaches for IBDP Mathematics
50
Paper 2 Section B – Optimization Problems
Example
In the figure, points A , B , C and D are on the circumference of a circle, centre O and
radius 1. AOB ˆ BOC ˆ
π
� � � , 0 ��
� .
2
(a) By considering ABC ˆ , show that ADC ˆ � � .
[3]
(b) Show that the area of OCDA is sin� if B , O and D are collinear.
[3]
(c) Consider the case when OAB is an equilateral triangle. Let AOD ˆ � � , 0 �� � �
and A be the area of OCDA .
(i) Express A in terms of � .
(ii)
(iii)
Hence, determine the maximum area of OCDA , justifying that this value
is a maximum.
Write down the value of � when A attains its maximum.
(iv)
Write down the range of values of A for
� 3�
��
� .
2 4
[12]
154
SE Production Limited