MathematicsFind the length of the tangent from an external point P   at a distance of 20 cm   from the centre of a circle of radius 12 cm.

Find the length of the tangent from an external point P   at a distance of 20 cm   from the centre of a circle of radius 12 cm.


10. Find the length of the tangent from an external point P at a distance of 20 cm from the centre of - Brainly.in

  1. A
        14cm
  2. B
        17cm
  3. C
        16cm
  4. D
        18cm 

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    Solution:

    Given that length of tangent is 20cm and radius of the circle is 12cm.
    10. Find the length of the tangent from an external point P at a distance of 20 cm from the centre of - Brainly.inWe know that the tangents are perpendicular to the radius of the circle.
    Therefore, ∠CDP = 90°.
    In ∆CDP, By Pythagoras theorem,
    (CD) 2 + (PD) 2 = (PC) 2 ⇒ (12) 2 + (PD) 2 = (20) 2 ⇒ (PD) 2 =400−144 ⇒ (PD) 2 =256 ⇒PD=16cm  
    Hence, the length of the tangent from an external point P is 16cm.
    Therefore, option 3 is correct.
     

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