\( A B C \) is a variable triangle such that \( A \) is \( (1,2) \), and \( B \) anc \( C \) lie...

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\( A B C \) is a variable triangle such that \( A \) is \( (1,2) \), and \( B \) anc \( C \) lie on the line \( y=x+\lambda(\lambda \) is a variable). Then the locus of the orthocenter of \( \triangle A B C \) is
(A) \( x+y=0 \)
(B) \( x^{2}+y^{2}=4 \)
(C) \( x-y=0 \)
(D) \( x+y=3 \)
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