A) \[1:\sqrt{2}\]
B) \[\sqrt{2}:1\]
C) \[(\sqrt{2}-1):1\]
D) \[1:(\sqrt{2}-1)\]
Correct Answer: D
Solution :
\[\frac{\text{Area}\,\,(\Delta ABC)}{\text{Area}\,\,(\Delta AXY)}=\frac{A{{B}^{2}}}{A{{X}^{2}}}\] \[\Rightarrow \] \[\frac{2\,\text{Area}\,\,(\Delta AXY)}{\text{Area}\,\,(\Delta AXY)}=\frac{A{{B}^{2}}}{A{{X}^{2}}}\] \[\Rightarrow \] \[\frac{2}{1}=\frac{A{{B}^{2}}}{A{{X}^{2}}},\frac{AB}{AX}=\sqrt{2}\] \[\Rightarrow \] \[AB=\sqrt{2}AX\] \[\Rightarrow \] \[AX+BX=\sqrt{2}AX\] \[\therefore \] \[BX=AX(\sqrt{2}-1)\Rightarrow \frac{AX}{BX}=\frac{1}{\sqrt{2}-1}\] \[\therefore \]\[X\]divides AB in 1 : \[(\sqrt{2}-1).\]You need to login to perform this action.
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