Question
Download Solution PDFএকটি ΔABC এর বাহু AB এবং AC-এর উপর D এবং E যথাক্রমে দুটি বিন্দু এমনভাবে অবস্থিত যে DE, BC-এর সমান্তরাল এবং AD ∶ DB = 7 ∶ 9। যদি CD এবং BE পরস্পরকে F বিন্দুতে ছেদ করে, তাহলে ΔDEF এবং ΔCBF এর ক্ষেত্রফলের অনুপাত নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
AD : DB = 7 : 9
DE ∥ BC
গণনা:
AD : DB = 7 : 9
সুতরাং, AD : AB = 7 : (7 + 9) = 7 : 16
ΔADE এবং ΔABC
∠ ADE = ∠ ABC --- (অনুরূপ কোণ)
∠ AED = ∠ ACB --- (অনুরূপ কোণ)
∠ A = ∠ A --- (সাধারণ কোণ)
সুতরাং, ΔADE ∼ ΔABC
AD : AB = DE : BC = 7 : 16
এখন,
ΔDEF এবং ΔBCF
∠ DEF = ∠ FBC ---(একান্তর কোণ)
∠ EDF = ∠ FCB ---(একান্তর কোণ)
∠ DFE = ∠ BFC --- (বিপ্রতীপ কোণ)
সুতরাং, ΔDEF ∼ ΔBCF
অতএব, ΔDEF এবং ΔCBF-এর ক্ষেত্রফল
⇒ DE2 : BC2
⇒ 72 : 162
⇒ 49 : 256
∴ সঠিক বিকল্প হল 3.
Last updated on Jul 23, 2025
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