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11th Class Mental Ability Geometry Question Bank Question - Geometry

  • question_answer
    In the adjoining figure of \[\Delta \mathbf{ABC}=\mathbf{12}{{\mathbf{0}}^{\mathbf{{}^\circ }}}\] and \[\mathbf{AB=c,}\,\mathbf{BC=a,}\,\,\mathbf{AC=b}\]then:

    A) \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}+ba\]

    B) \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}-ba\]

    C) \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ba\]

    D) \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}+2ba\]

    E) None of these

    Correct Answer: A

    Solution :

    Explanation Option (a) is correct. \[cos\text{ }C=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}\] \[-\frac{1}{2}=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}\] \[\Rightarrow \]   \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}+ab\]


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