Let the weight triangle ABC (CA = CB), the height BD. On the edges BA, BC take the two points E and F respectively so that BE = BF = BD. Via E, draw a straight line parallel to AC cut BC at N, cut BD at K. Pass F draw a straight line parallel to AC cut AB at M, cut BD at I.

Calculate the lengths of sides AB and BC if you know EM = 9cm, FN = 12cm and IK = 6cm.