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NTA Abhyas JEE Main2020MathematicsCirclePractice

If O is the origin and O P , O Q are distinct tangents to the circle x 2 + y 2 + 2 g x + 2 f y + c = 0 , then the circumcentre of the triangle O P Q is

Options

  1. A- g , - f
  2. Bg , f
  3. C- f , - g
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Tangents drawn from the point O , meet the cirle at P & Q and C be the centre of given circle. Then points O , P , C and Q are concyclic. That means any circle passing through O , P and Q also passes through C and O C is the diameter for this circle. Hence mid point of O C is the circumcentre of triangle O P Q . Coordinates of circumcenter = - g 2 , - f 2

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