9 . The following diagram shows a rectangle ABCD and a sector EBC of a circle
with centre E and radius r . E is the mid-point of AD . BE � r and ABE ˆ � � , π where 0 ��
� . 2
E
A r
r
�
B
D C
( a ) Express AB in terms of r and � . [ 1 ] r 2 sin 2� ( b ) Show that the area of the triangle ABE is . 4
[ 4 ]
( c ) Show that BEC ˆ � 2� .
[ 2 ] The ratio of the area of the triangle ABE to the area of the sector EBC is 1 : k if ABCD is a square .
( d ) Find k .
Consider a case when ABCD is not a square . The ratio of the area of the triangle ABE to the area of the sector EBC is 1 : 3 .
( e ) Find � .
[ 7 ]
[ 2 ]
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