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State Apollonius Theorem and Centroid di...

State Apollonius Theorem and Centroid divides circumcentre and orthocentre in 1:2

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Centroid divide line joining circumcenter and orthocenter in 1:2

Centroid divides each median in ratio 2:1

Knowledge Check

  • Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

    A
    Statement 1 is true, Statement 2 is true and Statement 2 is correct explanation for Statement 1.
    B
    Statement 1 is true , Statement 2 is true and Statement 2 is not the correct exlpanation for Statement 1.
    C
    Statement 1 is true, Statement 2 is false.
    D
    Statement 1 is false, Statement 2 is true.

  • In an equilateral triangle, incentre, circumcentre and orthocentre are

    A
    collinear
    B
    concyclic
    C
    coincide
    D
    none of these

  • Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation 5x-3y=0 Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio 1:2

    A
    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
    B
    Statement-1 is True, Statement-2 is True, Statement-2 not a correct explanation for Statement-1
    C
    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True

    • Similar Questions

    Explore conceptually related problems

    (1) If coordinates of centroid and circumcentre of a triangle are known, coordinates of its orthocentre can be obtained. (2) Centroid, circumcentre and orthocentre of a triangle are collinear. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

    If z_1,z_2,z_3 be the vertices A,B,C respectively of an equilateral trilangle on the Argand plane and |z_1|=|z_2|=|z_3| then (A) Centroid oif the triangle ABC is the complex number 0 (B) Distance between centroid and orthocentre of the triangle ABC is 0 (C) Centroid of the tirangle ABC divides the line segment joining circumcentre and orthcentre in the ratio 1:2 (D) Complex number representing the incentre of the triangle ABC is a non zero complex number

    Statement 1: If the vertices of a triangle are having rational coordinates,then its centroid, circumcenter,and orthocentre are rational. Statement 2: In any triangle,orthocentre, centroid,and circumcenter are collinear,and the centroid divides the line joining the orthocentre and circumcenter in the ratio 2:1.

    If A(0,1,2) B(2,-1,3) and C(1,-3,1) are the vertices of a triangle then the distance between circumcentre and orthocentre is

    What is the distance between circumcentre and orthocentre of a right angled triangle ?

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