AD is perpendicular to the internal bisector of ∠ABC of ΔABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is

Answer: Option D

∠ABD = ∠MBD = θ (angle bisector)
∴ SD ⊥ AM
∠BDA = ∠BDM = 90°
It happen only in equilateral and isosceles triangle
∴ AD = DM
i.e. AD = $$\frac{\text{AM}}{2}$$
Given DE || BC
From Thales theorem
E will be mid point of AC
∵ AC = 12 cm
So, AE = 6 cm