A) 3 : 2
B) 2 : 1
C) 3 : 1
D) 5 : 2
Correct Answer: B
Solution :
In \[\Delta DMN\] and \[\Delta BMC,\] |
DM = MC [Given] |
\[\angle 1=\angle 2\] [vertically opposite] |
\[\angle 3=\angle 4+\angle 9\] [Alternate interior angles] |
\[\Delta DMN=\Delta BME\] (as a) [Alternate interior angle] |
DN = BC = AD |
So, \[AN=2BC\] \[\Rightarrow \] \[\frac{AN}{BC}=\frac{2}{1}\] ?(i) |
In \[\Delta OAN\] and \[\Delta OBC,\] |
\[\angle 5=\angle 6\] [Vertically opposite] |
\[\angle 7=\angle 8\] [Alternate interior angle] |
\[\angle 9=\angle 10\] [Rest angle] |
\[\therefore \] \[\Delta OAN\sim \Delta OBC\] |
So, the sides will be in same ratio |
\[\frac{AN}{BC}=\frac{ON}{OB}\] |
\[\Rightarrow \] \[\frac{2}{1}=\frac{ON}{OB}\] [from Eq. (i)] |
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