\(BD=2\cdot R\cdot sinBAD\)
=>\(BD=\sqrt{\dfrac{1}{sin^2BAD}}\)
=>\(\dfrac{R}{2}=\dfrac{2}{3}\cdot\sqrt{7}\)
=>\(\dfrac{2}{3}\cdot\sqrt{7}\cdot sinBAD=\sqrt{1+\dfrac{1}{sin^2BAD}}\)
=>\(28sin^4BAD-9sin^2BAD-9=0\)
=>\(28sin^4BAD-21sin^2BAD+12sin^2BAD-9=0\)
=>\(7sin^2BAD\left(4sin^2BAD-3\right)+3\left(4sin^2BAD-3\right)=0\)
=>\(\left(4sin^2BAD-3\right)\left(7sin^2BAD+3\right)=0\)
=>\(4\cdot sin^2BAD-3=0\)
=>\(sin^2BAD=\dfrac{3}{4}\)
=>\(sinBAD=\dfrac{\sqrt{3}}{2}\)(Do \(0< \widehat{BAD}< 180^0\) nên \(sinBAD>0\))
=>\(\widehat{BAD}=60^0\)
=>Chọn D
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