| In the figure given below, if \[AB||DC\]and AC and PQ intersect each other at point O, then the value of \[OA.CQ\] is |
 |
A) \[OC\,.\,OQ\]
B) \[OP\,.\,OC\]
C) \[OC\,.\,AP\]
D) \[OQ\,.\,OP\]
Correct Answer: C
Solution :
| Given, \[AB\,|\,|\,DC\]and AC and PQ intersect each other at point O. |
| Now, in \[\Delta AOP\]and \[\Delta COQ\] |
| \[\angle AOP=\angle COQ\] [Vertical opposite angles] |
| \[\angle APO=\angle CQO\] |
| [\[\because\] alternate angle, \[AB\,\,|\,\,|\,\,\,DC\]and PQ is a transversal] |
| \[\therefore \Delta AOP\tilde{\ }\Delta COQ\] [from AAA similarity] |
| then, \[\frac{OA}{OC}=\frac{AP}{CQ}\] |
| [\[\because\] corresponding sides are proportional] |
| \[\Rightarrow \,\,OA\,.\,CQ=OC\,.\,AP\] |
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