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web-flow authored Jun 4, 2024
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Expand Up @@ -77,7 +77,6 @@ <h1 id="title">ICPC Notebook</h1>
<li><a class="section" href="#memo">memo</a></li>
<ol>
<li><a href="#Primes.md">Primes.md</a></li>
<li><a href="#math.md">math.md</a></li>
</ol>
</ol>
</nav>
Expand Down Expand Up @@ -789,28 +788,6 @@ <h4>階乗</h4>
<td>$4.8 \times 10^8$</td>
</tr>
</tbody></table>
</div>

<div class="filename">
<h2 id="math.md">math.md</h2>
</div>
<div class="content content-md"><h4>等式</h4>
<p>$\begin{aligned}ax+by=e \\ cx+dy=f\end{aligned}
\Rightarrow
\begin{aligned}x=\dfrac{ed-bf}{ad-bc},\ y=\dfrac{af-ec}{ad-bc}\end{aligned}$</p>
<h4>三角形</h4>
<ul>
<li>Side lengths: $a,b,c$</li>
<li>Semiperimeter: $p=\dfrac{a+b+c}{2}$</li>
<li>Area: $A=\sqrt{p(p-a)(p-b)(p-c)}$</li>
<li>Circumradius: $R=\dfrac{abc}{4A}$</li>
<li>Inradius: $r=\dfrac{A}{p}$</li>
<li>Length of median (divides triangle into two equal-area triangles): $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$</li>
<li>Length of bisector (divides angles in two): $s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$</li>
<li>Law of sines: $\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}=\dfrac{1}{2R}$</li>
<li>Law of cosines: $a^2=b^2+c^2-2bc\cos\alpha$</li>
<li>Law of tangents: $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$</li>
</ul>
</div>

</body>
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