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A circle is inscribed in a right triangle with legs of length 10 and 24. What is the radius of the circle?

1. 2
2. 4
3. 6
4. 8

Correct answer: 4

Solution

The hypotenuse is \(\sqrt{10^2+24^2}=26\). For a right triangle, the inradius is \(r=\frac{a+b-c}{2}=\frac{10+24-26}{2}=4\).

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