In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If AC = 4.2 cm, DC = 6 cm, BC = 10 cm,  find AB.

19 In fig. DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value x.                         
          20 In a Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 4 cm, AE = 8 cm, DB = x – 4
and EC = 3x – 19, find x. 22 In Δ ABC, ∠ B = 90° and D is the mid-point of BC. Prove that AC² = AD² + 3CD².
23 ABC is a triangle in which AB = AC and D is a point on the side AC such that BC² = AC × CD. Prove that BD = BC.