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Question Number 49362 by behi83417@gmail.com last updated on 06/Dec/18

Commented by behi83417@gmail.com last updated on 06/Dec/18

$as showen in picture, when this statement$ $is true ?$ ${FE}^{2} + {FD}^{2} = {BC}^{2}$
Commented by mr W last updated on 06/Dec/18

$w h e n A E = A D a n d F = H, i . e . E D$ $t a n g e n t s t h e c i r c l e .$
Commented by behi83417@gmail.com last updated on 06/Dec/18

$t h i s i s t r u e w h e n E D ∥ B C, e v e n i f : F \neq H .$ $r i g h t s i r ?$
Commented by mr W last updated on 06/Dec/18

$n o . t h i s i s t r u e o n l y E D / / B C a n d F = H .$
Commented by mr W last updated on 06/Dec/18

$I m i s r e a d t h e q u e s t i o n a s$ ${F E}^{2} + {H D}^{2} = {B C}^{2}$
Commented by behi83417@gmail.com last updated on 06/Dec/18

$y e s s i r . i s i t ⇑ t r u e i n s p e c i a l c a s e ?$
Commented by mr W last updated on 06/Dec/18

$y e s . t h e r e a r e a l s o i n f i n i t e p o s s i b i l i t i e s .$
	Answered by behi83417@gmail.com last updated on 06/Dec/18

	Commented by behi83417@gmail.com last updated on 06/Dec/18

	$∡ H D B = ∡ G E K = 45$ $∡ H G I = ∡ K G E = 45$ ${D G}^{2} = {D I}^{2} + {I G}^{2} = 2 {I G}^{2}$ ${G E}^{2} = {G K}^{2} + {K E}^{2} = 2 {K G}^{2}$ $\Rightarrow {D G}^{2} + {G E}^{2} = 2 ({I G}^{2} + {K G}^{2}) = 2 {A G}^{2} =$ $= 2 R^{2} = {B C}^{2} .$
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