Let A
2 be the difference between the area of the unit circle and the area of the inscribed pentagon PQ1QRR 1.
( b ) ( i ) Write down
1 ˆ Q OQ .
( ii ) Write down the exact area of the triangle Q1OQ in terms of � .
1 � 2� 2� � � � � � ( iii ) Hence , show that A2
� � �sin � � 2� �sin
� 2 � 3 3 � � 3 3 � . [ 5 ]
The points Q
1
, Q
2 and R
1, R
2 are constructed on the arc PQ and PR respectively such that PQ1 � Q1Q 2
� Q2Q � RR1 � R1R 2 � R2P
, as shown in the following diagram :
R
2
P Q
1
R
1
Q
2
O
R Q
Let A
3 be the difference between the area of the unit circle and the area of the inscribed heptagon PQ1Q 2QRR1R 2
.
( c ) ( i ) Find
2 ˆ Q OQ .
( ii ) Express A
3 in the form similar to the expression of A
2 in ( b )( iii ). [ 6 ]
The points Q
1
,..., Q n� 1 and R
1,..., Rn
� 1 are constructed on the arc PQ and PR respectively such that PQ1 � Q1Q 2
� ... � Qn�
1Q � RR1 � R1R 2
� ... � Rn�
1P
.
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