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Question Number 29048 by $@ty@m last updated on 03/Feb/18

Commented by ajfour last updated on 04/Feb/18

$t h a n k s f o r v e r i f y i n g S i r!$
Commented by $@ty@m last updated on 04/Feb/18

$S o r r y$ $I d o n t h a v e t h e a n s w e r .$
Commented by ajfour last updated on 04/Feb/18

$p l e a s e e x p l a i n S i r!$ $i t h i n k s o m e t h i n g w r o n g w i t h$ $q u e s t i o n . .$
Commented by ajfour last updated on 04/Feb/18

$S_{1} = S_{2} = A (s a y)$ $S_{1} + S_{2} = S_{3} + S_{4} = 2 A . . . (i)$ $3 (S_{1} + S_{3}) = S_{2} + S_{4}$ $\Rightarrow 3 A + 3 S_{3} = A + S_{4}$ $\Rightarrow 3 S_{3} + 2 A = S_{4}$ $u s i n g (i)$ $3 S_{3} + S_{3} + S_{4} = S_{4}$ $\Rightarrow S_{3} = 0 .$ $\Rightarrow O D = 0 .$ $w r o n g d a t a i n q u e s t i o n!$
Commented by ajfour last updated on 04/Feb/18

Commented by NECx last updated on 03/Feb/18

$s a t y a m . . . . . . i v e n o t s e e n y o u$ $o n l i n e f o r a l o n g w h i l e . I t f e e l s$ $c o o l t o s e e y o u b a c k h e r e o n t h e$ $f o r u m .$
Commented by $@ty@m last updated on 03/Feb/18

$I o p e n t h i s a p p e v e r y d a y b u t$ $m o s t o f t h e t i m e s I f a i l t o s o l v e$ $t h e p r o o b l e m s .$ $H o w e v e r I a m l e a r n i n g a l o t o n$ $t h i s p l a t f o r m .$
Commented by $@ty@m last updated on 03/Feb/18

$i n w h i c h c l a s s t e x t b o o k$ $c a n i f i n d t h i s t h e o r e m ?$
Commented by $@ty@m last updated on 03/Feb/18

Commented by $@ty@m last updated on 03/Feb/18

$i s i t o k a y n o w ?$
Commented by Tinkutara last updated on 03/Feb/18
BF=3. This is direct application of Ceva's Theorem.
Commented by Tinkutara last updated on 03/Feb/18
OD=4
Commented by Tinkutara last updated on 03/Feb/18

Commented by $@ty@m last updated on 03/Feb/18

$T h a n k s a l o t .$
Commented by Tinkutara last updated on 03/Feb/18
http://ibb.co/keD4G6
Commented by Tinkutara last updated on 04/Feb/18
OD=3 or 4? What is the answer? I am getting two different answers.
Commented by Tinkutara last updated on 04/Feb/18
This way it comes 3.
Commented by Tinkutara last updated on 04/Feb/18

Commented by mrW2 last updated on 04/Feb/18

$y o u a r e r i g h t s i r .$ $F o l l o w i n g r e l a t i o n s a r e v a l i d :$ $D C = 2 B D$ $A F = 2 B F$ $A O = 3 O D$
	Answered by mrW2 last updated on 04/Feb/18

	Commented by mrW2 last updated on 04/Feb/18

	$Δ C I E \sim Δ C D A$ $\Rightarrow C I = D I$ $Δ B O D \sim Δ B E I$ $\Rightarrow B D = D I$ $\Rightarrow D C = 2 B D$ $t h e r e f o r e {i t}^{'} s n o t p o s s i b l e t h a t$ $B D = 5 a n d D C = 15!$ $Δ A H E \sim Δ A F C$ $\Rightarrow A H = H F$ $Δ B F O \sim Δ B H E$ $\Rightarrow B F = F H$ $\Rightarrow A F = 2 B F$ $o r B F = \frac{A F}{2} = \frac{9}{2} = 4.5$ $O D = 2 I K$ $I K + K E = 2 O D$ $\Rightarrow \frac{O D}{2} + K E = 2 O D$ $\Rightarrow K E = \frac{3}{2} O D$ $A O = 2 K E$ $\Rightarrow A O = 3 O D$ $o r O D = \frac{A O}{3} = \frac{12}{3} = 4$
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