In an equilateral △ABC,AD ⊥BC, prove that \(AD^2=38D^2\),
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In an equilateral △ABC,AD ⊥BC, prove that \(AD^2=38D^2\),
In an equilateral △ABC,AD ⊥BC, prove that \(AD^2=38D^2\),
We have
⊿ ABC is an equilateral triangle and AD⊥BC
In ⊿ ADB⊿ ADC
∠ADB = ∠ADC = 90° AB = AC (Given)
AD = AD (Common)
⊿ ADB ≅⊿ ADC (By RHS condition)
∴ BD = CD = BC/2 ……. (i)
In ⊿ ABD
BC2 = AD2 + BD2
BC2 = AD2 + BD2 [Given AB = BC]
(2BD)2 = AD2 + BD2 [From (i)]
4BD2 – BD2 = AD2
AD2 = 3BD2