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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.

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  1. SheldonEinstein
    • 3 years ago
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    @mukushla

  2. SheldonEinstein
    • 3 years ago
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    OK what can I do is just draw a diagram on the basis of the given information first... wait

  3. waterineyes
    • 3 years ago
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    @mukushla is not online this time..

  4. UnkleRhaukus
    • 3 years ago
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    |dw:1352285181683:dw|

  5. UnkleRhaukus
    • 3 years ago
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    There it is!

  6. waterineyes
    • 3 years ago
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    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
    • 3 years ago
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    |dw:1352334002288:dw|

  8. waterineyes
    • 3 years ago
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    It is by the property of Semi circle..

  9. waterineyes
    • 3 years ago
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    And we are to find its coordinates.. And @UnkleRhaukus will solve this further... Ha ha ha...

  10. akash123
    • 3 years ago
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    Z(A), Z(B) and Z(c) are complex numbers?

  11. UnkleRhaukus
    • 3 years ago
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    It is by the property of Semi circle! thats right! |dw:1352285595958:dw|

  12. akash123
    • 3 years ago
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    Without loss of generality we can assume C is the origin ..it'll simplify the problem |dw:1352285727325:dw|

  13. akash123
    • 3 years ago
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    if Z(A), Z(B), Z(C) are complex numbers..

  14. akash123
    • 3 years ago
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    i have made some more assumption...AC=BC

  15. akash123
    • 3 years ago
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    otherwise use (Z-0)/(z0-0) ={ I z I / I Z0 I }e^( i pi/2)

  16. SheldonEinstein
    • 3 years ago
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    @amistre64 and @myininaya may share their ideas ...

  17. amistre64
    • 3 years ago
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    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|

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