question_answer

AB and CD are parallel line segments of lengths 8 cm and 7 cm respectively. If AD and BC intersect at O and AO = 16 cm, then OD is equal to

A)  14 cm  

B)  15 cm

C)  16cm

D)  18 cm

Correct Answer: A

Solution :

 From \[\Delta \,OAB\]and \[\Delta \,ODC\] \[\angle AOB=\angle DOC\] (opposite angles) \[\angle DAB=\angle ADC\] (alternate angles) and        \[\angle CBA=\angle DCB\] (alternate angles) \[\therefore \]  \[\Delta \,\,OAB\]and \[\Delta \,\,ODC\] are similar. \[\therefore \]  \[\frac{OD}{OA}=\frac{CD}{AB}\] or            \[OD=\frac{OA\times CD}{AB}\]                 \[=\frac{16\times 7}{8}=14\]