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?
+79 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.
