In a ∆ABC, the bisector of ∠CAB intersects BC at D and the circumcircle of ∆ABC at E. If AC : AE = 4 : 7, then what will be the ratio of AD : AB?

  1. 7 : 4
  2. 5 : 4
  3. 4 : 7
  4. 3 : 2

Answer (Detailed Solution Below)

Option 3 : 4 : 7
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F1 P.S Pallavi 28.11.19 D 11

AE is the angle bisector of ∠CAB.

⇒ ∠EAB = ∠CAE

Also ∠CBA = ∠CEA ( Angles subtended by chord AC on the circle)

⇒ ∆AEC ~ ∆ABD

⇒ AC/AE = AD/AB = 4/7

⇒ AD : AB = 4 : 7

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