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# help

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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

#1
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The radius of the circle is 12.

Jan 28, 2023
#2
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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.