Apps. and Interpretation for IBDP Maths Ebook 2 | Page 59

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Paper 1 – Areas and Perimeters of Segments
Example
The following diagram shows a circle with centre O and radius 120 cm .

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The points A , B and C are on the circumference of the circle , and AOB ˆ � 1.31 rad .
( a ) Find the exact length of arc ACB .
( b ) Find the length of AB .
( c ) Hence , find the perimeter of the shaded segment ABC .
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Solution
( a ) The exact length of arc ACB � ( 120 )( 1.31 )
( A1 ) for substitution
( b )
� 157.2 cm A1
2 2
AB � 120 �120 � 2 ( 120 )( 120 ) cos1.31 ( M1 )( A1 ) for substitution AB � 146.1982184 AB � 146 cm
A1
( c ) The required perimeter �146.1982184 � 157.2
( M1 ) for correct approach
� 303.3982184 � 303 cm
A1
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