等式
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$\begin{aligned}ax+by=e \\ cx+dy=f\end{aligned}
-\Rightarrow
-\begin{aligned}x=\dfrac{ed-bf}{ad-bc},\ y=\dfrac{af-ec}{ad-bc}\end{aligned}$
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三角形
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-- Side lengths: $a,b,c$
-- Semiperimeter: $p=\dfrac{a+b+c}{2}$
-- Area: $A=\sqrt{p(p-a)(p-b)(p-c)}$
-- Circumradius: $R=\dfrac{abc}{4A}$
-- Inradius: $r=\dfrac{A}{p}$
-- Length of median (divides triangle into two equal-area triangles): $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$
-- Length of bisector (divides angles in two): $s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$
-- Law of sines: $\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}=\dfrac{1}{2R}$
-- Law of cosines: $a^2=b^2+c^2-2bc\cos\alpha$
-- Law of tangents: $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$
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