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MHT CET202210 Aug 2022Evening ShiftMathematicsStraight LinesActual

The orthocentre and centroid of triangle are A(-3,5) and B(3,3) respectively. If C is the circumcenter of this triangle, then the radius of the circle having line segment A C as a diameter, is units.

Options

  1. A10
  2. B3 5 2
  3. C2 10
  4. D3 5 2

Correct answer

B. 3 5 2

Step-by-step solution

Circumcentre divides orthocentre A(-3,0) and centroid B(3,3) externally in the ratio 3:1 Hence, C ( 3 3-1 (-3) 3-1 , 3 3-1 5 3-1 ) (6,2) Now required radius = 1 2 A C= 1 2 (6+3)^2+(2-5)^2 =3 5 2

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