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