## SheldonEinstein 3 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.

1. SheldonEinstein

@mukushla

2. SheldonEinstein

OK what can I do is just draw a diagram on the basis of the given information first... wait

3. waterineyes

@mukushla is not online this time..

4. UnkleRhaukus

|dw:1352285181683:dw|

5. UnkleRhaukus

There it is!

6. waterineyes

If we draw a line from point C to the intersection point, the line will make 90 degrees and will be perpendicular to AB..

7. waterineyes

|dw:1352334002288:dw|

8. waterineyes

It is by the property of Semi circle..

9. waterineyes

And we are to find its coordinates.. And @UnkleRhaukus will solve this further... Ha ha ha...

10. akash123

Z(A), Z(B) and Z(c) are complex numbers?

11. UnkleRhaukus

It is by the property of Semi circle! thats right! |dw:1352285595958:dw|

12. akash123

Without loss of generality we can assume C is the origin ..it'll simplify the problem |dw:1352285727325:dw|

13. akash123

if Z(A), Z(B), Z(C) are complex numbers..

14. akash123

i have made some more assumption...AC=BC

15. akash123

otherwise use (Z-0)/(z0-0) ={ I z I / I Z0 I }e^( i pi/2)

16. SheldonEinstein

@amistre64 and @myininaya may share their ideas ...

17. amistre64

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|