MathematicsO is the center of a circle with a diameter 30 cm. P is a point outside the circle and PA is tangent of the circle, then find: (i) The length of tangent PA; if OP = 39 cm, (ii) The distance between O and P, if the length of the tangent PA is 20 cm.

O is the center of a circle with a diameter 30 cm. P is a point outside the circle and PA is tangent of the circle, then find: (i) The length of tangent PA; if OP = 39 cm, (ii) The distance between O and P, if the length of the tangent PA is 20 cm.


  1. A
    39 cm
  2. B
    36 cm
  3. C
    27 cm
  4. D
    25 cm 

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    Solution:

    IMG_256Given that diameter = 30cm
    As we know radius = diameter 2 =15 cm  
    Let's denote the radius of the circle by r i.e. r = 15 cm
    Since OP = 39 cm
    In ∆OPA as we know .
    Now we have a right triangle with sides
    OA (radius) = 15 cm, OP = 39 cm and PA
    As we know, Pythagorean theorem can be used in right triangle
    It follows,
    O A 2 +P A 2 =O P 2  
    Substituting the given values we get
    (15) 2 +P A 2 = (39) 2 P A 2 =1521225 P A 2 =1296 PA= 1296 PA=36cm  
    AP = 36cm
    So, the correct answer is Option 2.
     
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