A) \[\frac{OA}{OC}=\frac{OB}{OD}\]
B) \[\frac{AB}{OC}=\frac{OA}{OC}\]
C) \[\angle OAB=\angle ODC\]
D) \[\frac{OA}{OB}=\frac{OC}{OD}\]
Correct Answer: A
Solution :
(a): Draw ABCD is a trapezium and AC and BD are diagonals intersect at O. In figure, \[AB\parallel DC\] (Given) \[\Rightarrow \]\[\angle 1=\angle 3,\angle 2=\angle 4\] (Alternate interior angles) Also, \[\angle DOC=\angle BOA\] (Vertically opposite angles) \[\Rightarrow \]\[\Delta \,OCD\tilde{\ }\Delta \,OAB\] (Similar triangle) \[\Rightarrow \]\[\frac{OC}{OA}=\frac{OD}{OB}\] (Ratio of the corresponding sides of the similar triangles) \[\Rightarrow \]\[\frac{OA}{OC}=\frac{OB}{OD}\] (Taking reciprocals) Hence proved.You need to login to perform this action.
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