A) \[PQ||AB\]
B) \[PQ\ne AB\]
C) \[\frac{QB}{CQ}=\frac{PA}{CP}\]
D) None of the above
Correct Answer: B
Solution :
Given, \[CQ=25\,\,cm\], \[CB=30\,\,cm\], |
CP = 10 cm and CA = 16 cm |
Here, \[\frac{CQ}{CB}=\frac{25}{30}=\frac{5}{6}\] and \[\frac{CP}{CA}=\frac{10}{16}=\frac{5}{8}\Rightarrow \,\,\,\frac{CQ}{CB}\ne \frac{CP}{CA}\] |
\[\Rightarrow \,\,\,\frac{CB}{CQ}\ne \frac{CA}{CP}\Rightarrow \,\,\frac{CB}{CQ}-1\ne \frac{CA}{CP}-1\] |
\[\Rightarrow \,\,\,\frac{CB-CQ}{CQ}\ne \frac{CA-CP}{CP}\] |
\[\Rightarrow \,\,\,\frac{QB}{CQ}\ne \frac{PA}{CP}\]or \[\frac{CQ}{QB}\ne \frac{CP}{PA}\] |
Hence, by converse of basic proportionality theorem, PQ is not parallel to AB. |
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