MathematicsIn the given figure , R Q  is a chord of the circle and P O Q is its diameter such that ∠RPO= 30 °  . If O T is the tangent to the circle at the point O  , then find ∠ROT  .

In the given figure , R Q  is a chord of the circle and P O Q is its diameter such that RPO= 30 °  . If O T is the tangent to the circle at the point O  , then find ROT  .


  1. A
        40 °  
  2. B
        30 °  
  3. C
        60 °  
  4. D
        70 °   

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    Solution:

    Gicen that RQ is a chord of the circle and POQ is the diameter and RPO= 30 °  .
    We know that angle inscribed in the semicircle is right angle.
    So, PRQ= 90 °  
    In ΔPQR  ,
    By angle sum property,
      PRQ+RPQ+PQR= 180 ° 90 ° + 30 ° +PQR= 180 ° PQR=180°90°30° PQR=60  
    Now, the tangents are perpendicular to the radius of the circle.
    Therefore, PQT= 90 °  
    Compute the RQT   by subtracting the value of PQR   from PQT   RQT=PQTPQR RQT= 90 ° 60 ° RQT=30°  
    Hence, the value of RQT   is 30 °  .
    Therefore option 2 is correct.
     
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