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9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    In \[\Delta \mathbf{ABC}\], \[\mathbf{AB}=\mathbf{a}-\mathbf{b},\mathbf{AC}=\sqrt{{{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}}\]and \[\mathbf{BC}=\sqrt{2\mathbf{ab}}\], then find single B.

    A)  \[{{60}^{{}^\circ }}\]                                   

    B)  \[{{30}^{{}^\circ }}\]

    C)  \[{{90}^{{}^\circ }}\]    

    D)  \[{{45}^{{}^\circ }}\]

    Correct Answer: C

    Solution :

    (c): \[AB=a-b:BC=\sqrt{2ab;}\] \[AC=\sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\therefore A{{B}^{2}}+B{{C}^{2}}={{(a-b)}^{2}}+{{\left( \sqrt{2ab} \right)}^{2}}\] \[={{a}^{2}}+{{b}^{2}}-2ab+2ab={{a}^{2}}+{{b}^{2}}=A{{C}^{2}}\] \[\therefore \]\[\angle ABC={{90}^{{}^\circ }}\]                      


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