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How to Find the Radius of a Circle Inscribed in a Triangle

by Chance E. Gartneer, Demand Media

    A circle that is inscribed in a triangle is a circle inside the triangle with a circumference, or perimeter, that touches all of the triangle's sides. The radius of an inscribed circle does not only measure the length from its center to its circumference, but also measures the distance from the circle's center to each of the triangle's sides. You can find the radius of a triangle's inscribed circle through the lengths of its sides.

    Items you will need

    • Calculator
    Step 1

    Add the lengths of the sides together and then halve the sum. For example, the side lengths are 3, 4 and 5. Those numbers added together equals 12, and 12 divided by 2 equals 6.

    Step 2

    Subtract the lengths of the sides individually from the sum calculated in Step 1 and then multiply the differences together. For this example, 6 minus 3 equals 3, 6 minus 4 equals 2 and 6 minus 5 equals 1. 3, 2 and 1 multiplied together equals 6.

    Step 3

    Multiply the amount calculated in Step 2 by the amount calculated in Step 1 and then find the square root of that number. For this example, 6 multiplied by 6 equals 36. The square root is 6.

    Step 4

    Divide the square root from Step 3 by the amount calculated in Step 1. For this example, 6 divided by 6 equals 1. The radius of the circle inscribed in the triangle is 1.

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    About the Author

    Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

    Photo Credits

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