# How to Find the Radius of a Circle Inscribed in a Triangle ••• PeopleImages/E+/GettyImages

When a student is attempting to discern the radius of a circle that is inscribed in what is an obvious triangle, it can create a perplexing problem. It would appear to be a simple solution to a basic geometry question using lessons learned through math courses previously attended over years of study. The surrounding frame may be obvious but what lies between can cause a conundrum. Discerning the radius is a matter of a few equations that once known can open a world of possibilities in many math areas.

## Calculating the Circumference of a Circle

First, know your basics. Understanding how to calculate the circumference of a circle is a must. Don’t confuse it with how to calculate the perimeters of other objects in geometry. The perimeter is the distance around a shape, such as a rectangle or square. The circle has its own set of verbiage. The distance around the entire circle is the circumference.

The diameter is the space from one equal side of the circle to another, or the line that is drawn straight through the circle, subsequently cutting the circle in even halves. The radius is half of the diameter, or the space from the middle of the diameter to the outer circle’s edges. The radius is the most powerful building block for understanding other measurements of the circle. It gives the most information that can be manipulated to figure out other data. It gives its circumference, diameter, area and volume.

## How to Find Measurements of a Triangle

The area of a triangle can be found using the length and height of just one side. This length is called the base, or b for short, and the height is labeled h. The height forms a right angle with the base. The formula to find the area of a triangle is A=1/2xbxh. Once you have all the information needed, you can find the total area of a triangle.

## Pull It All Together

Let’s use a triangle with sides the length of 3, 4 and 5 as an example. The circle is inscribed in the triangle. Each side is tangent to the actual circle. Now the radius needs to be revealed to work the rest of the question to find a correct answer. The radius measures the length from its center to its circumference as well as the distance from the circle’s center to each of the triangle’s sides. Locate the radius of the triangle’s inscribed circle through measuring the lengths of its sides.