[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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