Analysis and Approaches for IBDP Maths Ebook 1 | Page 133

Front Page
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Paper 2 Section B – Problems of circles and sectors
Example
Consider a circle with centre O and radius 12 cm. Triangle ABC is drawn such that its
vertices are on the circumference of the circle.
AB � 16.8 cm , BC � 21.5 cm and BAC ˆ � 1.11 radians.
(a) Find ˆ ACB.
(b) Find AC .
(c) Hence or otherwise, find the length of arc ABC .
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Solution
11
(a)
(b)
sin ACB ˆ sin BAC ˆ
�
AB BC
(M1) for sine rule
sin ACB ˆ sin1.11
�
16.8 21.5
(A1) for substitution
ACB ˆ � 0.775250179
ACB ˆ � 0.775 radians
A1 N2
ABC ˆ � � �0.775250179 � 1.11
(M1) for valid approach
ABC ˆ � 1.256342474
A1
2 2 2
AC � AB � BC � 2(AB)(BC)cos ABC ˆ
(M1) for cosine rule
2 2 2
AC �16.8 � 21.5 � 2(16.8)(21.5)cos1.256342474 (A1) for substitution
AC � 22.82660156
AC � 22.8 cm
A1 N3
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