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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, ST is a tangent to the circle at F and QR h a diameter of the circle. If\[\angle RPT={{55}^{{}^\circ }}\], then the value of \[\angle SPC\]is

    A)  \[{{35}^{{}^\circ }}\]        

    B)  \[{{60}^{{}^\circ }}\]

    C)  \[{{80}^{{}^\circ }}\]                                   

    D)  \[{{100}^{{}^\circ }}\]

    Correct Answer: A

    Solution :

    (a): \[\angle RPT={{55}^{{}^\circ }}\] \[\angle RPQ={{90}^{{}^\circ }}\]  (Angle of semi circle) \[\angle TPS={{180}^{{}^\circ }}\] \[\therefore \] \[\angle SPQ={{180}^{{}^\circ }}-{{55}^{{}^\circ }}-{{90}^{{}^\circ }}={{35}^{{}^\circ }}\]                          


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