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In the figure below, ABCD is a trapezium. AB is parallel to DC, diagonals AC and DB intersect at X and DC=2AB.
AB=a, DA=d, AX=kAC and DX=hDB, where h and k are constants.
(a) Find in terms of a and d:
(i) BC
(ii) AX
(iii) DX
(b) Determine the values of h and k.