Let the acute triangle ΔABC have an outer circumscribed circle, whose tangents at the points B and C intersect at point P. Let D and E be the projections of perpendicular lines from point P on AC and AB. Prove that the interdection point of the heights of ΔADE is the midpoint of BC


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Question Number 181125 by depressiveshrek last updated on 21/Nov/22

$L e t t h e a c u t e t r i a n g l e Δ A B C h a v e$ $a n o u t e r c i r c u m s c r i b e d c i r c l e,$ $w h o s e t a n g e n t s a t t h e p o i n t s B a n d C$ $i n t e r s e c t a t p o i n t P . L e t D a n d E b e$ $t h e p r o j e c t i o n s o f p e r p e n d i c u l a r$ $l i n e s f r o m p o i n t P o n A C a n d A B .$ $P r o v e t h a t t h e i n t e r d e c t i o n p o i n t o f$ $t h e h e i g h t s o f Δ A D E i s t h e m i d p o i n t$ $o f B C$
Commented by mr W last updated on 22/Nov/22

$p l e a s e c h e c k t h e q u e s t i o n!$ $i n t e r s e c t i o n p o i n t o f h e i g h t s o f$ $Δ A D E = o r t h o c e n t e r o f Δ A D E ?$ $i t s e e m s t h a t o r t h o c e n t e r o f Δ A D E$ $i s n o t t h e m i d p o i n t o f B C . y o u c a n$ $c h e c k w h e n y o u m a k e a d r a w i n g .$
Commented by depressiveshrek last updated on 22/Nov/22

$I a l s o f i n d t h e q u e s t i o n t o b e c o n f u s i n g,$ $t h e i n t e r s e c t i o n i s c l e a r l y n o t t h e$ $m i d p o i n t o f B C$
Commented by mr W last updated on 22/Nov/22

$i c h e c k e d a g a i n . t h e q u e s t i o n i s$ $c o r r e c t . s o r r y!$
	Answered by mr W last updated on 22/Nov/22

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