Problem based on centroid| Orthocentre| Circumcentre| Ambigous case

Assertion: If coordinates of the centroid and circumcentre oif a triangle are known, coordinates of its orthocentre can be found., Reason: Centroid, orthocentre and circumcentre of a triangle are collinear. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Three vertices of a triangle are A(4,3);B(1,-1) and C(7,k). Value(s) of k for which centroid,orthocentre,incentre and circumcentre of the Delta ABC lie on the same straight line is/are-

Let P be a point interior to the acute triangle ABC. If PA+PB+PC is a null vector,then w.r.t traingel ABC, point P is its a.centroid b. orthocentre c.incentre d.circumcentre

The sides of a triangle are 9 cm, 40 cm and 41 cm. The distance between its orthocentre and circumcentre is

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 a triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1:2 ,

Let the line joining through orthocentre and circumcentre of the triangle ABC is parallel to the base BC .If tan B=k cot C then the value of k is equal to

(3,2),(-4,1) and (-5,8) are vertices of triangle then select the CORRECT alternative/s orthocentre is (4,1) orthocentre is (-4,1) circumcentre is (-1,5) circumcentre is (3,2)

In an equilateral triangle prove that the centroid and the centre of the circumcircle (circumcentre) coincide.