Question

Draw a triangle ABC of base BC = 5.6 cm, ∠A = 40° and the bisector of ∠A meets BC at D such that CD = 4 cm.

Answer 1

Construction:

Steps (1) Draw a line segment BC = 5.6 cm.

Steps (2) At B, draw BE such that ∠CBE = 60°.

Steps (3) At B draw BF such that ∠EBF = 90°.

Steps (4) Draw ⊥^r bisector to BC, which intersects
BF at 0.

Steps (5) With O as centre and OB as radius draw a circle.

Steps (6) From C, mark an arc of 4 cm on BC at D.

Steps (7) The ⊥^r bisector intersects the circle at I. 

Join ID.

Steps (8) ID produced meets the circle at A.

Now join AB and AC. ΔABC is the required triangle