Скачать или смотреть Animated proof of Inradius Area Formula

Proof of Inradius Area Formula.

We can start with a triangle ABC.

We're going to draw a bisector from each angle. This is a line that splits the angle in half. The point where they meet will be the center point of our incircle.

The incircle touches each line at one point, and the center point of the circle is the intersection of all the bisectors.

Now, we need to find the radius of the circle. We're going to make a line from the center of the incircle perpendicular to each line in the triangle. The length of any of these lines is the inradius.

The length of the radius can be used to find the area.

Calculating the Area

Recall the equation for the semi-perimeter, S = a+b+c/2. We can multiply this by the length of the inradius to find the area.

A = S • R

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