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In an equilateral triangle ABC,D is a point on side BC such that BD=1(bc)/3, prove that 9AD^2=7AB^2

Posted by Amal Majumder 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Priyanshu Singh Pratap 6 years, 1 month ago

Given that ∆ABC is a equilateral ∆ so AB=CB=BA To prove = 9AD^2=7AB^2 Proof- BD=bc/3 , dc=bc/2 And , angle adc=adb=90° By pgt , Ab^2=ad^2+bd^2 , ad^2=Ab^2-bd^2 (1).. Similiarly, ad^2=ac^2-dc^2 (2)... From(1)&(2).. Ab^2-bd^2=ac^2-dc^2 And, ab^2-(bc/3)^2=ac^2-(bc/2)^2 After solving it we get , 9Ad^2=7ab^2

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CBSE > Class 10 > Mathematics