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    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: AC┬▓ = AD┬▓ + CD┬▓ - 2 ├Ч AD ├Ч CD ├Ч cos 60┬░, AC┬▓ = 10┬▓ + 9┬▓ - 2 ├Ч 10 ├Ч 9 ├Ч 1/2, AC┬▓ = 100 + 81 - 90, AC┬▓ = 91, AC = тИЪ91 тЙИ 9.53 cm. Answer: c) 9.5 cm.

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