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?Solution
The triangle is a right triangle with sides in a 3:4:5 ratio. The area A = (1/2) × base × height = (1/2) × 12 × 16 = 96 cm². 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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