MathematicsThe length of the tangents from a point A to a circle of radius 3cm is 4cm. The distance (in cm) of A from the center of the circle is:

The length of the tangents from a point A to a circle of radius 3cm is 4cm. The distance (in cm) of A from the center of the circle is:

  1. A
    7
  2. B
    7
  3. C
    5
  4. D
    25  

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    Solution:

    Given a circle with radius 3cm and length of tangent 4 cm.
    Drawing the required figure,
    We use the fact that tangent is perpendicular to radius at the point of contact.
    Using Pythagoras theorem in ΔOBA,
    AO2=OB2+AB2
    AO2=32+42
    AO=32+42
    AO=5cm So, the distance of the point A from the center of the circle is 5cm.
    Therefore, option (3) is correct.
     
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