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SheldonEinstein
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A( \(z_A\) ) , B ( \(z_B\) ) , C ( \(z_C\) ) are vertices of right angled triangle, \(z_c\) being the orthocentre. A circle is described on AC as diameter. Find the point of intersection of the circle with hypotenuse.
 2 years ago
 2 years ago
SheldonEinstein Group Title
A( \(z_A\) ) , B ( \(z_B\) ) , C ( \(z_C\) ) are vertices of right angled triangle, \(z_c\) being the orthocentre. A circle is described on AC as diameter. Find the point of intersection of the circle with hypotenuse.
 2 years ago
 2 years ago

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SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.0
@mukushla
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.0
OK what can I do is just draw a diagram on the basis of the given information first... wait
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.1
@mukushla is not online this time..
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
dw:1352285181683:dw
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
There it is!
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.1
If we draw a line from point C to the intersection point, the line will make 90 degrees and will be perpendicular to AB..
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.1
dw:1352334002288:dw
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.1
It is by the property of Semi circle..
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.1
And we are to find its coordinates.. And @UnkleRhaukus will solve this further... Ha ha ha...
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.0
Z(A), Z(B) and Z(c) are complex numbers?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
It is by the property of Semi circle! thats right! dw:1352285595958:dw
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.0
Without loss of generality we can assume C is the origin ..it'll simplify the problem dw:1352285727325:dw
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.0
if Z(A), Z(B), Z(C) are complex numbers..
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.0
i have made some more assumption...AC=BC
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.0
otherwise use (Z0)/(z00) ={ I z I / I Z0 I }e^( i pi/2)
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.0
@amistre64 and @myininaya may share their ideas ...
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
if i were to add anything, and im not sure how to read the notation in the problem; so i cant determine if the complex stuff is appropriate or not, but dw:1352297044749:dw
 2 years ago
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