Question

in an equilateral triangle ABC if AN⊥BC,prove that AN²=3BN²

Answer 1

$\frac{ \sqrt{3} }{4}{(bc)}^{2} = \frac{1}{2} bc \times an$
$\frac {\sqrt {3} }{2}{(bc)} = an$
${\sqrt {3} }{(bc)} =2(an)$
${3}{(bc)}^{2} = 4 {(an)}^{2}$
$12 {(bn)}^{2} = 4{(an)}^{2}$
$3 {(bn)}^{2} = {(an)}^{2}$