In triangle ABC , AD is perpendicular to BC. Prove that AD2= 3DC....tried the question many tyms...cn sum1 pls explain with the steps.

thankyou...

Here given triangle ABC must be an equilateral triangle and we have to prove AD2 =  3DC2

Solution:

Given: ∆ABC is an equilateral, AD ⊥ BC.

 

 

In right ∆ABD,
AB2 = BD2 + AD2
⇒ BC2 = BD2 + AD2   (AB = BC)
⇒ (2BD)2 = BD2 + AD2   [From (1)]
⇒ 4BD2 = BD2 + AD2
⇒ AD2 = 3BD2 = 3DC2  [As BD = DC]

Hence proved

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