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Question Number 13067 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/May/17

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/May/17

$i n t r i a n g l e A B C :$ $i) ∡ B I A = ∡ C I B = ∡ A I C$ $i i) D E ⊥ B C, D F ⊥ A C, D H ⊥ A B$ $i i i) S_{A B C} = 1 (a r e a o f Δ A B C)$ $1) I D = ?$ $2) \frac{D E}{A I} + \frac{D H}{C I} + \frac{D F}{B I} = ?$ $3) i f S_{A H D F} = S_{C F D E} + S_{B H D E} \Rightarrow ∡ H D F = ?$ $(S_{A H D F} = a r e a o f A H D F)$
Commented by mrW1 last updated on 13/May/17

$T h e p o s i t i o n o f I i s u n i q u e l y d e f i n e d,$ $b u t t h e p o s i t i o n o f D i s n o t u n i q u e l y$ $d e f i n e d, t h e r e f o r e I D c o u l d b e a n y$ $v a l u e .$ $∡ H D F = 180 ° - ∡ A, t h i s i s a l w a y s t r u e .$
Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/May/17

$a d d i t i o n a l c o n d i t i o n s :$ $B E = E C, D E = 1 .$ $s p e c i a l c a s e : D ≅ I$ $n o t e : I, D, E, a r e n o t c o l l i n e a r i n g e n e r a l .$
Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/May/17

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