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JEE Main2018MathematicsProperties of TrianglesActual

Let the orthocentre and centroid of a triangle be A - 3 , 5 and B 3 , 3 respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment A C as diameter, is:

Options

  1. A3 5 2
  2. B10
  3. C2 10
  4. D3 5 2

Correct answer

D. 3 5 2

Step-by-step solution

Centroid B divides the line joining Orthocentre A and circumcentre C in the ratio 2 : 1 A B =   3 + 3 2 + 5 - 3 2 =   6 2 + 2 2 =   40 = 2 10 A C = 3 2 × 2 10 = 3 10 Radius = A C 2 = 3 10 4 = 3 5 2

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