The frame shown below is supported by a pin at A and a roller at B$.$

$($a$)$ Draw complete free body diagrams of $($i$)$ the entire frame, $($ii$)$ member ACE, $($iii$)$ member BCD$.$

$($b$)$ Determine the reactions at the supports at A and B$.$

$($c$)$ Determine the components of reaction at $C$ and the resultant force at $C$ using one of the member free body diagrams in $($a$).$

$($d$)$ Confirm that the member not analyzed in $($c$)$ is in equilibrium using your answers from $($b$)$ and $($c$),$ ie show that all forces and moments add to zero on the FBD not used in part $($c$).$