2022 VJC P1 Q2
The diagram shows triangle $ABC$, where angle $ACD=\left( \frac{\pi }{4}+x \right)$ radians. Point $D$ is on $BC$ such that $AD=2$ and $BD=2\sqrt{3}$.
Show that if $x$ is sufficiently small for ${{x}^{3}}$ and higher powers of $x$ to be neglected, then
$BC\approx k\left( 1+\sqrt{3}-2x+2{{x}^{2}} \right)$,
where $k$ is a constant to be determined.
[5]
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