If A(z1),B(z2) and C(z2) are the three points in argand plane where |z1+z2|=|z1|−|z2| and |(1−i)z1+iz3|=|z1|+|z3−z1|, then-
A
A,B and C lie on a fixed circle with centre (z2+z32)
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B
A,B,C form right angle triangle
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C
A,B,C form an equilateral triangle
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D
A,B,C form an obtuse angle triangle
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Solution
The correct options are AA,B and C lie on a fixed circle with centre (z2+z32) BA,B,C form right angle triangle arg(z1z2)=±π&|z1+i(z3−z1)|=|z1|+|z3−z1|⇒arg(z1z3−z1)=π2 So, centre of circle =(z2+z32) and △ABC is a right angled triangle