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AD is perpendicular to the internal bisector of ABC of ABC...

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Geometry
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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 & Solution
Correct Answer: Option D
Geometry mcq question image
∠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
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