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The diagram shows a trapezium \(A B C D\) in which \(B C\) is parallel to \(A D\) and angle \(B C D = 90 ^ { \circ }\). The coordinates of \(A , B\) and \(D\) are \(( 2,0 ) , ( 4,6 )\) and \(( 12,5 )\) respectively.
- Find the equations of \(B C\) and \(C D\).
- Calculate the coordinates of \(C\).