Problem #$2[20$ pts$].$ A chain $($DE$)$ is wrapped around a gear in the diagram. The member ABC pivots on a pin at A and a force at $B$ generates tension in the chain.

a$.$ What is the chain tension?

b$.$ What are the forces that the gear places on member ABC at $C$ assuming its diameter is $10$ inches? $($Note: the cable is tangent to the gear as it heads to $D$ and $E$ from the gear, i$.$e$.,$ it makes a $90$ angle with the radius of the gear at that location. Please ask if you are not sure about the angle that the chain makes with the radius of the gear.$)$

$T_{\text{D}\text{C}\text{E}}=$

$C_x=$

$C_y=$