A) \[\sqrt{10}\]
B) \[10\]
C) \[5\sqrt{2}\]
D) \[5\]
Correct Answer: C
Solution :
The intersection point of line \[y=7x-25\] and circle \[{{x}^{2}}+{{y}^{2}}=25\] is \[{{x}^{2}}+{{(7x-25)}^{2}}=25\] \[\Rightarrow \] \[50{{x}^{2}}-350x+600=0\] \[\Rightarrow \] \[{{x}^{2}}-7x+12=0\] \[\Rightarrow \] \[(x-3)(x-4)=0\] \[\Rightarrow \] \[x=3,\,x=4\] and \[y=-4,3\] \[\therefore \] Coordinates of \[A(3,-4)\] and \[B(4,3)\] \[\therefore \] Length, \[AB=\sqrt{{{(4-3)}^{2}}+{{(3+4)}^{2}}}\] \[=\sqrt{1+49}=5\sqrt{2}\]
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