Column - I | Column - II | ||
P. | \[\frac{AD}{DB}\] | 1. | \[\frac{AC}{AE}\] |
Q. | \[\frac{AB}{AD}\] | 2. | \[\frac{AE}{EC}\] |
R. | \[\frac{DB}{AB}\] | 3. | \[\frac{AB}{AC}\] |
S. | \[\frac{AD}{AE}\] | 4. | \[\frac{EC}{AC}\] |
A) P-1, Q-2, R-3, S-4
B) P-4, Q-3, R-2, S-1
C) P-2, Q-1, R-4, S-3
D) P-1, Q-3, R-2, S-4
Correct Answer: C
Solution :
In \[\Delta \,ABC,\]\[BC\,\,|\,\,|\,\,DE\] |
(P) \[\frac{AD}{DB}=\frac{AE}{EC}\left( BPT \right)\] |
(Q) \[\frac{AD}{DB}=\frac{AE}{EC}\] |
\[\Rightarrow \frac{DB}{AD}=\frac{EC}{AE}\Rightarrow \frac{DB}{AD}+1=\frac{EC}{AE}+1\] |
\[\Rightarrow \frac{BD+AD}{AD}=\frac{EC+AE}{AE}\Rightarrow \frac{AB}{AD}=\frac{AC}{AE}\] |
(R) Similarly, \[\frac{DB}{AB}=\frac{AB}{AC}\] |
(S) \[\frac{AD}{AB}=\frac{AE}{AC}\Rightarrow \frac{AD}{AE}=\frac{AB}{AC}\] |
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