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SheldonEinstein
 2 years ago
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.
SheldonEinstein
 2 years ago
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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0if 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
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