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MHT CET202619 April 2026Evening ShiftMathematicsCircleActual

Let PA and PB be the tangent segments drawn from point P (6, 8) to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

Options

  1. A5
  2. B5 2
  3. C5 2
  4. D5 2

Correct answer

B. 5 2

Step-by-step solution

Let the radius of the circle be r . The centre of the circle is O(0, 0) and the external point is P(6, 8) . The distance between O and P is: OP = (6-0)^2 + (8-0)^2 = 36 + 64 = 100 = 10 The length of the tangent segments PA and PB from P to the circle is: PA = PB = OP^2 - r^2 = 100 - r^2 The quadrilateral PAOB consists of two congruent right-angled triangles, OAP and OBP . The area of the quadrilateral PAOB is: A = 2 Area of OAP = 2 ( 1 2 OA PA ) = r 100 - r^2 To maximize the area A , we can maximize its square, A^2

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