Assertion :Number of solutions of complex number z satisfying |z−1−2i|=|z−2−3i|=|z−3| is one Reason: If z1≠z2≠z3, then |z−z1|=|z−z2|=|z−z3| has one solution.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is C Assertion is correct but Reason is incorrect Locus of z satisfying |z−1−2i|=|z−2−3i|=|z−3| will be the circumcentre of triangle with vertices (1,2),(2,3),(3,0) where as |z−z1|=|z−z2|=|z−z3| can have no solution when z1,z2,z3 are collinear.