Mathematics
Grade9
Easy

Question

Find the length of the tangent to a circle with center ‘O’ and radius = 6 cm from a point p such that OP = 10 cm.

  1. 25 cm
  2. 8 cm
  3. 10 cm
  4. None of the above

hintHint:

In the given question there is a point p outside the circle from where a line touches the circle at a point which is a tangent . We know that the angle formed with the radius of the circle and tangent to the circle is right angle. So a right angled triangle is formed where hypotenuse, the line from the point p to center of the circle O, and perpendicular, radius of the circle, is given so by using pythagoras theorem we can find base i.e. the tangent to the circle.

The correct answer is: 8 cm


    Given, OP (hypotenuse)= 10cm, radius(perpendicular) =6 cm
    by pythagoras theorem,
    h to the power of 2 space end exponent equals p squared plus b squared
rightwards double arrow 10 squared equals 6 squared plus b squared
rightwards double arrow 100 equals 36 plus b squared
rightwards double arrow b squared equals 100 minus 36
rightwards double arrow space b squared space space equals 64
rightwards double arrow b equals 8 space c m
    So the length of the tangent from point p is 8 cm.

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