1 . You are asked to investigate the inscribed polygon in a semicircle . In this question , all angles are measured in degrees .
An inscribed triangle AP1
B is constructed in a semicircle of radius 1 and centred at O , where arc AP1 � arc PB
1
, as shown in the following diagram :
P
1
A O
B
Let R ( 2 ) and L ( 2 ) be the area of the triangle AP1
B and the length AP
1 respectively .
( a ) Find arc P1
B , giving the answer in terms of � .
( b ) Write down
[ 2 ]
( i ) R ( 2 ) ;
( ii ) L ( 2 ). [ 2 ]
The points P
1 and P
2 are constructed on the arc length of the semicircle such that arc AP1 �arc PP
1 2
� arc P2
B , as shown in the following diagram :
P
1
P
2
A O
B
Let R ( 3 ) and L ( 3 ) be the area of the quadrilateral AP1P 2B and the length AP
1 respectively .
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