11 . PQR is a triangle such that PQ � � r and PR � � q . S is a point on QR such that PS � QR . Let QS : SR � 1 : � , where � � 1.
� � �
( a ) By considering PS �PQ� QS, express PS � in terms of � , q and r .
[ 4 ] q�( r �q) ( b ) Show that � � r � ( q � r ) . [ 4 ]
( ( )) ( ( )) ( c ) Hence , show that PS � r � r �q q � q� r �q r
� .
2 r�q
Suppose that PQR is a right-angled triangle such that
�
QPR ˆ � 90 , PQ � 15
[ 6 ]
� and PR � 20 .
( d ) ( i ) Find � .
( ii ) Hence , find the area of the triangle PSR . [ 7 ]
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