Answer:
Both at points A and B, the path difference between the waves coming from \[{{S}_{1}}\] and \[{{S}_{2}}\] will be \[\lambda /2\]. Hence destructive interference occurs at A and B. As \[{{S}_{1}}C={{S}_{2}}C,\] the path difference between the waves reaching the point \[C\]from \[{{S}_{1}}\] and \[{{S}_{2}}\] will be zero. Hence constructive interference occurs at point C.
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