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Right triangle TRI has side lengths 20, 21, 29. A circle is drawn inside triangle TRI that is tangent to all three sides.



What is the radius of the circle?

 Jan 28, 2023
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The radius of the circle is 12.

 Jan 28, 2023
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That's the diameter of the circle.

 

Using the formula \(r=\dfrac{\text{Area of triangle}}{\text{semiperimeter}}\) and heron's formula, we can find the inradius.

 

The semiperimeter is \(s=35\), so using \(A=\sqrt{35(35-20)(35-21)(35-29)}\), we have \(A=210\). Dividing by \(s=35\), we get the inradius 6.

 

The radius is 6.

Elephant200  Jan 28, 2023

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