A circle is inscribed in a right triangle with legs of length 5 and 12. What is the radius of the circle?
2
Step 1 – find the hypotenuse:
\(c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13\)
Step 2 – use the inradius formula for a right triangle:
For a right triangle with legs \(a,\ b\) and hypotenuse \(c\), the inradius is \(r = \dfrac{a + b - c}{2}\).
\(r = \dfrac{5 + 12 - 13}{2} = \dfrac{4}{2} = 2\)
Hence the radius of the inscribed circle is 2.
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