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Question Number 68183 by ajfour last updated on 06/Sep/19

Commented by ajfour last updated on 06/Sep/19

$Q B C a n d B P D a r e t a n g e n t a n d$ $n o r m a l r e s p e c t i v e l y t o$ $t h e c u b i c f u n c t i o n y = x^{3} - 19 x + 30$ $a t o n e o f i t s r o o t a n d Q A D a n d$ $A P C a r e a g a i n t a n g e n t a n d$ $n o r m a l r e s p e c t i v e l y t o t h e$ $s a m e f u n c t i o n a t o n e o f i t s o t h e r$ $r o o t . C i r c u m c i r c l e s a r e d r a w n$ $t o q u a d r i l a t e r a l s A B C D a n d$ $A P B Q . F i n d t h e i r r a d i i a n d$ $p r o v e t h a t P Q i s ⊥ t o C D .$
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