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Question Number 6553 by Rasheed Soomro last updated on 01/Jul/16

Commented by Rasheed Soomro last updated on 01/Jul/16

$∙ ∣ A B ∣= c, ∣ B C ∣= a, ∣ C A ∣= b$ $∙ \overset{\leftrightarrow}{A E}, \overset{\leftrightarrow}{B F}, \overset{\leftrightarrow}{C D} a r e a n g u l a r b i s e c t o r s$ $o f ∠ A, ∠ B, ∠ C r e s p e c t i v e l y .$ $★ ∣ D E ∣= f = ?, ∣ E F ∣= d = ?, ∣ F D ∣= e = ?$ $★ A r e a o f p o l y g o n L M N O P Q = ?$
Commented by Rasheed Soomro last updated on 01/Jul/16

$S e r i e s o f q u e s t i o n s o f g e n e r a l t r i a n g l e$ $(s i m i l a r t o a b o v e) i s c o m p l e t e d w i t h$ $t h i s l a s t q u e s t i o n . T h e l i s t i s g i v e n b e l o w :$ $∙ T r i a n g l e w i t h m e d i a n l i n e s$ $∙ T r i a n g l e w i t h a l t i t u d e l i n e s$ $∙ T r i a n g l e w i t h a n g u l a r b i s e c t o r l i n e s$ $Thanks to forum - friends for cooperation!$
Commented by Yozzii last updated on 04/Jul/16

$F o r t h e p a r t c o n c e r n i n g t h e a r e a o f t h e$ $p o l y g o n, i t c a n b e f o u n d b y (1) f i n d i n g t h e$ $t o t a l a r e a o f t h e^{'} {g e n e r a t e d}^{'} t r i a n g l e$ $t h a t l i e s o u t s i d e t h e o r i g i n a l t r i a n g l e$ $a n d t h e n (2) s u b t r a c t f r o m t h e a r e a o f$ $t h e g e n e r a t e d t r i a n g l e t h e r e s u l t o f (1) .$ $B y t h e v e c t o r a n a l y s i s I s h a r e d o n$ $o n e o f y o u r p o s t s, {y o u}^{'} d n e e d t o f i n d$ $t h e v e r t i c e s o f e a c h o f t h e e x t e r n a l$ $t r i a n g l e s, c a l c u l a t e t h e s i d e s o f e a c h$ $t r i a n g l e a n d a p p l y {H e r o n}^{'} s f o r m u l a (o r u s e$ $a n y o t h e r m e t h o d f o r f i n d i n g t h e a r e a o f a t r i a n g l e$ $g i v e n i t s s i d e l e n g t h s)$ $f o r e a c h t o f i n d t h e t o t a l a n s w e r f o r$ $p a r t (1) . T h i s m e t h o d I^{'} v e d e s c r i b e d w o r k s$ $b u t i t i s r a t h e r l o n g t o t y p e h e r e g i v e n t h e$ $m u l t i t u d e o f a s s u m p t i o n s a n d c o n d i t i o n s$ $t h a t w o u l d n e e d t o b e d e l i n e a t e d i n a$ $f o r m a l a n s w e r .$
Commented by Yozzii last updated on 04/Jul/16

Commented by Yozzii last updated on 04/Jul/16

$H e r e, t h e r e a r e t w o e x t e r n a l t r i a n g l e s .$ $Y o u r d i a g r a m h a s t h r e e e x t e r n a l t r i a n g l e s .$ $T h i s d i a g r a m i s b a s e d o n a n g l e b i s e c t o r s .$
Commented by Yozzii last updated on 04/Jul/16

Commented by Yozzii last updated on 04/Jul/16

$H e r e, t h e r e i s o n e e x t e r n a l t r i a n g l e .$
Commented by Rasheed Soomro last updated on 04/Jul/16

$TH a n k S f o r g o o d a n a l y s i s o f t h e p r o b l e m$ $a n d g u i d i n g t o a w a y o f s o l u t i o n .$
Commented by Rasheed Soomro last updated on 04/Jul/16

$∙ T h e p r o b l e m s c a n b e e x t e n d e d t o a n y$ $n - s i d e d p o l y g o n i n a v a r i e t y o f w a y s!$ $∙ A l s o t h e y c a n b e e x t e n d e d t o a g e n e r a l$ $p o l y g o n .$
Commented by Yozzii last updated on 04/Jul/16

$Y e s y e s .$
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