Inradius of a Triangle: Definition, Formulas, and Applications

Inradius is the radius of a circle inscribed within a triangle. It is the distance from the center of the circle to any point on the circle. The inradius is also known as the "incenter" or "inscribed radius".

The inradius of a triangle can be found using various methods, including:

1. Law of cosines: The inradius of a triangle can be found using the law of cosines if the lengths of all three sides are known.
2. Area formula: The inradius of a triangle can be found using the area formula if the length of one side and the height of the triangle are known.
3. Incenter method: The incenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. The inradius can be found by taking the distance from the incenter to any point on the circle.
4. Heron's formula: Heron's formula is a formula for the area of a triangle that can be used to find the inradius.
5. Trigonometric methods: There are several trigonometric methods that can be used to find the inradius of a triangle, such as using the sine or cosine of one of the angles.

The inradius is an important concept in geometry and is used in many applications, including computer graphics, engineering, and architecture.