(I) Given,
\[AO\text{ }=\text{ }2CO\text{ }and\text{ }BO\text{ }=\text{ }2DO,\]
\[AO/CO\text{ }=\text{ }2/1\text{ }=\text{ }BO/DO\]
What’s more,
\[\angle AOB\text{ }=\angle DOC\] [Vertically inverse angles]
Consequently, \[\vartriangle AOB\text{ }\sim\text{ }\vartriangle COD\][SAS model for similarity]
(ii) As, \[AO/CO\text{ }=\text{ }2/1\text{ }=\text{ }BO/DO\][Given]
Consequently,
\[OA\text{ }x\text{ }OD\text{ }=\text{ }OB\text{ }x\text{ }OC\]