Question

    In a cyclic quadrilateral ABCD, where AB = 7 cm, BC = 8

    cm, CD = 9 cm, and DA = 10 cm, find the length of the diagonal AC if the angle between AB and DA is 60°.
    A 12 cm Correct Answer Incorrect Answer
    B 11.5 cm Correct Answer Incorrect Answer
    C 9.5 cm Correct Answer Incorrect Answer
    D 8.5 cm Correct Answer Incorrect Answer

    Solution

    Using the cosine rule in triangle ACD: AC² = AD² + CD² - 2 × AD × CD × cos 60°, AC² = 10² + 9² - 2 × 10 × 9 × 1/2, AC² = 100 + 81 - 90, AC² = 91, AC = √91 ≈ 9.53 cm. Answer: c) 9.5 cm.

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