A) \[\text{BC}.\text{EF}=\text{AC}.\text{FD}\]
B) \[AB.\text{EF}=\text{AC}.\text{DE}\]
C) \[\text{BC}\text{.DE}=\text{AB}.\text{EF}\]
D) \[\text{BC}\text{.DE}=\text{AB}.\text{FD}\]
Correct Answer: C
Solution :
[c] Given. \[\Delta ABC\tilde{\ }\Delta EDF\] |
\[\therefore \,\,\,\,\,\,\,\,\frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{EF}\] |
Taking first two terms, |
we get \[\frac{AB}{ED}=\frac{BC}{DF}\] |
\[\Rightarrow \,\,AB\cdot DF=ED\cdot BC\] or \[BC\cdot DE=AB\cdot FD\] |
So, option [d] is true. |
Taking last two terms, we get |
\[\frac{BC}{DF}=\frac{AC}{EF}\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,BC\cdot EF=AC\cdot DF\] |
So. option [a] is true. |
Taking first and last terms, we get |
\[\frac{AB}{ED}=\frac{AC}{EF}\,\,\,\,\,\,\,\Rightarrow \,\,\,\,AB\cdot EF=ED\cdot AC\] |
Hence, option [b] is true. |
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