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Assertion A : If - 1 , 3 , 2 and 5 , 3 , 2 are respectively the orthocentre and circumcentre of a triangle, then 3 , 3 , 2 is its centroid. Reason R : Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1 : 2 . Which one of the following is true?

Options

  1. AA and R are true and R is the correct explanation to A
  2. BA and R are true but R is not the correct explanation to A
  3. CA is true, R is false
  4. DA is false, R is true

Correct answer

C. A is true, R is false

Step-by-step solution

( A ) : Orthocentre is A - 1 , 3 , 2 Circumcentre is B 5 , 3 , 2 Centroid is C 3 , 3 , 2 The point C divides the line joining of A B in the ratio 2 : 1 internally, then Centroid = 2 5 + 1 - 1 2 + 1 , 2 3 + 1 3 2 + 1 , 2 2 + 1 2 2 + 1 = 10 - 1 3 , 6 + 3 3 , 4 + 2 3 = 3 , 3 , 2 ∴   A is true and R is false.

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