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A triangle ABC is such that a circle passing through vertex C, centroid G touches side AB at B. If AB = 6, BC = 4 then The length of median through A is equal to k then the value of k is

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answer is 42.

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Detailed Solution

Let median through A meet BC at D and circle at F Let GD=x,DF=y then AG⋅AF=AB22x(3x+y)=36xy=4 3x2+4=18x2=143  So, AD=3x=42
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