#### Beta Flash Shit Battor Face

08/08/2017 at 21:15-
a) We have :

\(\left\{{}\begin{matrix}\widehat{ADH}=90^0\\\widehat{DAE}=90^0\\\widehat{AEH}=90^0\end{matrix}\right.\)

So , quadrilateral DHEA is the rectangle

=> AH = DE (2 diagonals)

It also means : OD = OH = OE = OA (with O is the intersection)

b) Consider \(\Delta ODI\) and \(\Delta OHI\) , we have :

DI = IH

*(DI is the median of square triagle BDH)*DO = OH

IO general

=> \(\Delta ODI\) = \(\Delta OHI\) (e - e - e)

=> \(\widehat{IDO}=90^0\Rightarrow DE\perp ID\) (1)

Similar with \(\Delta OHK\) and \(\Delta OEK\)

\(\Delta OHK\) = \(\Delta OEK\) (e - e - e)

=> \(\widehat{OEK}=90^0\Rightarrow DE\perp EK\) (2)

From (1) and (2)

=> DI // EK

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