Three vertices of a triangle are \( \mathrm{A}(4,3) ; \mathrm{B}(1,...

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Three vertices of a triangle are \( \mathrm{A}(4,3) ; \mathrm{B}(1,-1) \) and \( \mathrm{C}(7, \mathrm{k}) \). Value(s) of \( \mathrm{k} \) for which centroid, orthocentre, incentre and circumcentre of the \( \triangle \mathrm{ABC} \) lie on the same straight line is/are-
\( \mathrm{P} \)
(A) 7
(B) \( -1 \)
(C) \( -19 / 8 \)
(D) none
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