TargetIIT

Good prob flicked from another forum:

Given complex numbers a,b,c,d such that [im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7Ba-d%7D%7Bb-c%7D[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7Bb-d%7D%7Bc-a%7D[/im] are purely imaginary, prove that [im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7Bc-d%7D%7Ba-b%7D[/im] is also purely imaginary

Let A, B, C be the geometric image of the complex numbers a, b, c. And let D be the orthocenter of triangle ABC. Then assigning the complex number d to D satisfies the given first two conditions and the third one easily follows.

yres sir i got it
threee points are used to  form a triangle
and the fact that altitudes are concurrent
sir am i right ?

[image]38435044.jpg[/image]

yes..