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9th Class Mathematics Quadrilaterals Question Bank Quadrilateral

  • question_answer
    ABCD is a cyclic quadrilateral and O is the centre of the circle. If \[\angle \mathbf{COD}=\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\]and \[\angle \mathbf{BAC}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\], then the value of \[\angle \mathbf{BCD}\] is equal to

    A)  \[{{70}^{{}^\circ }}\]                                   

    B)  \[{{90}^{{}^\circ }}\]

    C)  \[{{60}^{{}^\circ }}\]     

    D)  \[{{80}^{{}^\circ }}\]

    Correct Answer: C

    Solution :

    (c): The angle subtended at the centre by an arc is twice to that of angle subtended at the circumference. \[\therefore \]\[\angle CAD=\frac{1}{2}\angle COD={{60}^{{}^\circ }}\] \[\therefore \angle BAD={{60}^{{}^\circ }}+{{60}^{{}^\circ }}={{120}^{{}^\circ }}\] \[\therefore \] \[\angle BCD={{180}^{{}^\circ }}-{{120}^{{}^\circ }}={{60}^{{}^\circ }}\]


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