Construct a ΔABC in which AB = 6.5 cm, ∠B = 60° and BC = 5.5 cm. Also construct a triangle AB‘C’ similar to ΔABC, whose each side is 3/2 time. The coresponding sides of triangle ABC

Steps of Construction:

(i) Construct a ΔABC in which AB = 6.5 cm, ∠B = 60°, BC = 5.5 cm.
(ii)    At B draw an acute angle CBX below base BC.
(iii)    Along BX, mark off points B₁, B₂, B₃, such that BB₁ = B₁ B₂ = B₂ B₃.
(iv)    Join B₂C.
(v)    From B₃ draw B₃C’ || B₂C meeting produced part of BC at C.
(vi)    From C’, draw C’ A’ || C    A intersecting the extended line segment BA at A’.

Thus, A’B’C’ is the required triangle each of whose sides is 3/2 times the corresponding sides of the triangle ΔABC.

Construction Based on tangent to a circle