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    Question

    A circle is inscribed in a triangle ABC with sides 12

    cm, 16 cm, and 20 cm. What is the radius of the circle?┬а
    A 2 cm Correct Answer Incorrect Answer
    B 3 cm Correct Answer Incorrect Answer
    C 4 cm Correct Answer Incorrect Answer
    D 5 cm Correct Answer Incorrect Answer

    Solution

    The triangle is a right triangle with sides in a 3:4:5 ratio. The area A = (1/2) ├Ч base ├Ч height = (1/2) ├Ч 12 ├Ч 16 = 96 cm┬▓. The semiperimeter s = (12 + 16 + 20) / 2 = 24 cm. The inradius r = A / s = 96 / 24 = 4 cm. Correct answer: c) 4 cm

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