Triangle Theorems

[Credit to Abel Martinez Foronda for the picture]

Well, you managed to my set about circles, and are now probably confused why I am talking about triangles. Well, triangles and circles are related. You can inscribe or circumscribe a circle into any triangle. This is because any circle is defined by three points, and a triangle has three points. Here are two very useful formulas to know about triangles and circles.

$K=rs\\ K=\frac { abc }{ 4R }$

Where $K$ is the area of the triangle, $s$ is the semi-perimeter, $a,b,c$ are the side lengths of the triangle, $r$ is the radius of the inscribed circle, and $R$ is the radius of the circumscribed circle.

These have many applications. The next couple problems after this note will be about these formulas.

This is part of the set Circles, made by Chris H.

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$