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    Question

    In triangle ABC, the sides are 5 cm, 12 cm, and 13 cm.

    Find: (a) the area of the triangle, (b) the inradius (radius of inscribed circle), (c) the circumradius (radius of circumscribed circle).
    A Area = 50 cm², Inradius = 2 cm, Circumradius = 5.5 cm Correct Answer Incorrect Answer
    B Area = 30 cm², Inradius = 2 cm, Circumradius = 6.5 cm Correct Answer Incorrect Answer
    C Area = 30 cm², Inradius = 8 cm, Circumradius = 6.5 cm Correct Answer Incorrect Answer
    D Area = 10 cm², Inradius = 2 cm, Circumradius = 16.5 cm Correct Answer Incorrect Answer

    Solution

    Sides 5,12,13 ⇒ right-angled triangle (5² + 12² = 13²), right angle at vertex opposite side 13. (a) Area = (1/2) × 5 × 12 = 30 cm² Semi-perimeter s = (5 + 12 + 13)/2 = 30/2 = 15 (b) Inradius r: r = Area / s = 30 / 15 = 2 cm (c) Circumradius R for any triangle: R = (abc) / (4 × Area) = (5 × 12 × 13) / (4 × 30) = 780 / 120 = 6.5 cm.

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