The diagram shows a block of mass 10 kg suspended below a horizontal ceiling by two strings AC and BC, of lengths 0.8 m and 0.6 m respectively, attached to fixed points on the ceiling. Angle ACB = 90°. There is a horizontal force of magnitude F N acting on the block. The block is in equilibrium.

\((a) In the case where F = 20, find the tensions in each of the strings.\)

(b) Find the greatest value of F for which the block remains in equilibrium in the position shown.