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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, two circles \[{{C}_{1}}\] and \[{{C}_{2}}\] touch each other internally at P. Two lines PCA and PCB meet the circles \[{{\mathbf{C}}_{1}}\] in C, D and \[{{\mathbf{C}}_{2}}\] in A, B respectively. If \[\angle \mathbf{BDC}=\mathbf{13}{{\mathbf{0}}^{{}^\circ }}\], then the value of \[\angle \]ABP is equal to

    A)  \[{{50}^{{}^\circ }}\]   

    B)  \[{{80}^{{}^\circ }}\]

    C)  \[{{100}^{{}^\circ }}\]                          

    D)  \[{{120}^{{}^\circ }}\]

    Correct Answer: A

    Solution :

    (a): \[\angle BDC={{130}^{{}^\circ }}\] \[\therefore \]\[\angle CDP={{180}^{{}^\circ }}-{{130}^{{}^\circ }}={{50}^{{}^\circ }}\] \[CD\parallel AB\] \[\therefore \] \[\angle ABP={{50}^{{}^\circ }}=\angle CDP\]                       


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