1 . You are asked to investigate the difference between the area of a unit circle and the area of an inscribed polygon .
An inscribed equilateral triangle PQR is constructed in a unit circle , as shown in the following diagram :
P
O
R
Q
P , Q and R are fixed point on the circumference such that QR is horizontal .
Let A
1 be the difference between the area of the unit circle and the area of the equilateral triangle PQR .
( a ) ( i ) Write down ˆ POQ .
( ii ) Show that A
1 can be expressed as
� 1 �� 2� 2�
� � �1�� �sin
� � 2 �� 3 3 � . [ 4 ]
The points Q
1 and R
1 are constructed on the arc PQ and PR respectively such that PQ1 � Q1Q � RR1 � R1P
, as shown in the following diagram :
P
R
1
Q
1
O
R Q
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