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Question Number 16464 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 22/Jun/17

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 22/Jun/17

$A \overset{Δ}{B C}, i s e q u i l a t e r a l a n d^{'} K^{'} i s a p o i n t$ $o n c i r c u m c i r c l e o f i t . d r a w K H, K J, K L$ $p a r a l l e l t o {A B C}^{'} s s i d e s a s s h o w e n .$ $1) p r o v e t h a t :$ $K J = K H + K L$ $2) d r a w i n g K L & K J, m a k e s 3 r e g i o n s$ $i n t r i a n g l e A B C, t h a t w e n a m e t h i s$ $r e g i o n s a s : S_{1} < S_{2} < S_{3} . f i n d m a x i m u m$ $o f r a t i o : \frac{S_{3}}{S_{1} + S_{2}}, w h e n^{'} K^{'}, m o v e s f r o m$ $\overset{}{m i d p o i n t} o f \overset{}{K B} t o m i d p o i n t o f K A .$ $S_{1} = a r e a o f r e g i o n n o . 1$
Commented by mrW1 last updated on 23/Jun/17

$Δ HLJ is equilateral,$ $\Rightarrow KH + KL = KJ, see Q . 16409$ $\max . \frac{S_{3}}{S_{1} + S_{2}} = \frac{\frac{7}{9}}{\frac{1}{9} + \frac{1}{9}} = \frac{7}{2} ? ? ?$
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