10th Class Mathematics Circles Question Bank Circles

  • question_answer
    A tangent ST at P to a circle at P is parallel to a chord QR of the circle. Which of the following is correct statement?

    A)  P is equidistant from the extremities of the chord.

    B)  PT is the tangent parallel to the chord PQ.

    C)  PT is the tangent parallel to the cord PR.

    D)  S is equidistant from the extremities of the chord.

    Correct Answer: A

    Solution :

     \[\therefore \]                                 .....(1) (Angle between tangent and chord is equal to the angle in the alternate segment.) \[\text{224}=\text{12}0\times \text{1}+\text{1}0\text{4}\]                                      ......(2) (Alternate angles as \[\text{12}0=\text{1}0\text{4}\times \text{1}+\text{16}\].) \[\text{1}0\text{4}=\text{16}\times \text{6}+\text{8}\] \[16=8\times 2+0\]                                   ....... (2) [From statements 1 and 2.] \[\text{256}=\text{8}\times \text{32}+0\] PQ = PR \[3465={{3}^{2}}\times 5\times 7\times 11\] P is equidistant from Q and R, the extremities of the chord.


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