∆ABC-তে, ∠CAB-এর দ্বিখণ্ডক BC-কে D বিন্দুতে এবং ∆ABC-এর পরিবৃত্তকে E বিন্দুতে ছেদ করে। যদি AC : AE = 4 : 7 হয়, তাহলে AD : AB-এর অনুপাত কত হবে?

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

Answer (Detailed Solution Below)

Option 3 : 4 : 7
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Detailed Solution

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F1 P.S Pallavi 28.11.19 D 11

AE হল ∠CAB-এর কোণ দ্বিখণ্ডক।

⇒ ∠EAB = ∠CAE

এছাড়াও ∠CBA = ∠CEA (বৃত্তে জ্যা AC দ্বারা উৎপন্ন কোণ)

⇒ ∆AEC ~ ∆ABD

⇒ AC/AE = AD/AB = 4/7

⇒ AD : AB = 4 : 7

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