2. Questions Bank
  3. 9th Class
  4. Mathematics
  5. Circles

9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure above, O is the centre of the circle. The line UTV is a tangent to the circle at T, \[\angle \mathbf{VTR}=\mathbf{5}{{\mathbf{6}}^{{}^\circ }}\]and \[\Delta \mathbf{PTR}\] is an isosceles triangle such that TP = TR. \[\angle \mathbf{x}+\angle \mathbf{y}+\angle \mathbf{z}\]is equal to?

    A)  \[{{175}^{{}^\circ }}\]                      

    B)  \[{{208}^{{}^\circ }}\]           

    C)  \[{{214}^{{}^\circ }}\]                                  

    D)  \[{{250}^{{}^\circ }}\]

    Correct Answer: D

    Solution :

    (d):- \[x=\angle VTR={{56}^{{}^\circ }}\] (Since, PTMR is a cyclic quadrilateral, \[x+z={{180}^{{}^\circ }}\] \[\Rightarrow {{56}^{{}^\circ }}+z={{180}^{{}^\circ }}\]    \[\Rightarrow \]\[z={{124}^{{}^\circ }}\] In \[\Delta PTR,\]      \[PT=TR\]               \[x=\angle 1={{56}^{{}^\circ }}\] \[\angle PTU=\angle 1={{56}^{{}^\circ }}\Rightarrow \angle QTU=y+{{56}^{{}^\circ }}\] \[\Rightarrow \]\[{{90}^{{}^\circ }}=y+{{56}^{{}^\circ }}\Rightarrow y={{34}^{{}^\circ }}\] \[\therefore \]\[x+y+z={{56}^{{}^\circ }}+{{34}^{{}^\circ }}+{{124}^{{}^\circ }}={{214}^{{}^\circ }}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner