Question
Download Solution PDFΔABC की भुजाओं AB और AC पर क्रमशः D और E बिंदु इस प्रकार हैं कि DE, BC के समानांतर है और AD ∶ DB = 7 ∶ 9 है। यदि CD और BE एक दूसरे को F पर प्रतिच्छेद करते हैं, तो ΔDEF और ΔCBF के क्षेत्रफलों का अनुपात ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
AD : DB = 7 : 9
DE ∥ BC
गणना:
AD : DB = 7 : 9
अतः, AD : AB = 7 : (7 + 9) = 7 : 16
ΔADE और ΔABC में
∠ ADE = ∠ ABC --- ( संगत कोण )
∠ AED = ∠ ACB --- ( संगत कोण )
∠ A = ∠ A --- (उभयनिष्ठ कोण)
अतः, ΔADE ∼ ΔABC
AD : AB = DE : BC = 7 : 16
अब,
ΔDEF और ΔBCF में
∠ DEF = ∠ FBC ---(एकांतर कोण)
∠ EDF = ∠ FCB ---(एकांतर कोण)
∠ DFE = ∠ BFC --- ( विपरीत कोण)
अतः, ΔDEF ∼ ΔBCF में
इस प्रकार, ΔDEF और ΔCBF के क्षेत्र
⇒ DE2 : BC2
⇒ 72 : 162
⇒ 49 : 256
∴ सही विकल्प 3 है
Last updated on Jun 13, 2025
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