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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below. O is the centre of the circle. AC and BD intersect at P. If \[\angle \mathbf{AOB}=\mathbf{11}{{\mathbf{0}}^{{}^\circ }}\] and \[\angle \mathbf{DAP}=\mathbf{3}{{\mathbf{0}}^{{}^\circ }}\], then \[\angle \mathbf{APB}\] is equal to

    A)  \[{{77}^{{}^\circ }}\]                       

    B)  \[{{80}^{{}^\circ }}\]   

    C)  \[{{85}^{{}^\circ }}\]                                   

    D)  \[{{90}^{{}^\circ }}\]

    Correct Answer: B

    Solution :

    (b):- Since, \[\angle ADB=\frac{1}{2}\angle AOB={{55}^{{}^\circ }}\] In \[\Delta DPA,\angle DAP+\angle ADP+\angle DPA={{180}^{{}^\circ }}\] \[\Rightarrow \]\[{{25}^{{}^\circ }}+{{55}^{{}^\circ }}+\angle DPA={{180}^{{}^\circ }}\Rightarrow \angle DPA={{100}^{{}^\circ }}\] Also, DPB be a straight line. \[\angle DPA+\angle APB={{180}^{{}^\circ }}\] \[\Rightarrow \angle APB={{180}^{{}^\circ }}-{{100}^{{}^\circ }}={{80}^{{}^\circ }}\]        


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