Home
Class 10
MATHS
If G be the centroid of a triangle ABC, ...

If G be the centroid of a triangle ABC, prove that, `AB^2 + BC^2 + CA^2 = 3(GA^2 + GB^2 + GC^2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONSTRUCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|32 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    RD SHARMA ENGLISH|Exercise All Questions|391 Videos

Similar Questions

Explore conceptually related problems

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

In any triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + BD^2) , where D is the midpoint of BC.

AD is a median of triangle ABC. Prove that : AB+BC+AC gt 2AD

If G is the centroid of a DeltaABC , then GA^(2)+GB^(2)+GC^(2) is equal to

P and Q are the mid-points of the CA and CD respectively of a triangle ABC, right angled at C. Prove that: 4AQ^2 = 4AC^2 + BC^2 , 4BP^2 = 4BC^2 + AC^2 , and 4(AQ^2 + BP^2) = 5AB^2 .

lf G be the centroid of a triangle ABC and P be any other point in the plane prove that PA^2+PB^2+PC^2=GA^2+GB^2+GC^2+3GP^2

In the following figure, OP, OQ and OR are drawn perpendiculars to the sides BC, CA and AB repectively of triangle ABC. Prove that : AR^(2)+BP^(2)+CQ^(2)=AQ^(2)+CP^(2)+BR^(2)

Construct a triangle ABC given that : BC = 4 . 5 cm, AB = 5 . 2 cm and CA = 3 . 8 cm

In a tetrahedron OABC, the edges are of lengths, |OA|=|BC|=a,|OB|=|AC|=b,|OC|=|AB|=c. Let G_1 and G_2 be the centroids of the triangle ABC and AOC such that OG_1 _|_ BG_2, then the value of (a^2+c^2)/b^2 is

If G is the centroid of triangle with vertices A(a,0),B(-a,0) and C(b,c) then (AB^(2)+BC^(2)+CA^(2))/(GA^(2)+GB^(2)+GC^(2))=

RD SHARMA ENGLISH-COORDINATE GEOMETRY-All Questions
  1. The perimeter of a triangle with vertices (0,4), (0,0) and (3,0) is

    Text Solution

    |

  2. A point P divides the line segment joining the points A(3,-5)a n dB(-4...

    Text Solution

    |

  3. If G be the centroid of a triangle ABC, prove that, AB^2 + BC^2 + CA...

    Text Solution

    |

  4. If A(-3,5),B(-2,-7),C(1,-8)a n dD(6,3) are the vertices of a quadrilat...

    Text Solution

    |

  5. The line segment joining the points P(3,3)a n dQ(6,-6) is trisected at...

    Text Solution

    |

  6. If the area of A B C formed by A(x , y),B(1,2)a n dC(2,1) is 6 squae ...

    Text Solution

    |

  7. Show that the points (a , a),(-a ,-a) and (-sqrt(3)a ,sqrt(3)a) are th...

    Text Solution

    |

  8. The x-coordinate of a point P is twice its y-coordinate. If P is eq...

    Text Solution

    |

  9. If A(4,-6),B(3,-2) a n d C(5,2) are the vertices of A B C, and AD is...

    Text Solution

    |

  10. Three vertices of a parallelogram ABCD are A(3,-4),B(-1,-3)a n dC(-6,2...

    Text Solution

    |

  11. Two uniform spheres A (Hollow) and B (solid) of same radius R (<r/2) a...

    Text Solution

    |

  12. Let ABCD be a square of side 2a. Find the coordinates of the vertices ...

    Text Solution

    |

  13. Find the coordinates of the vertices of an equilateral triangle of sid...

    Text Solution

    |

  14. The area of the triangle formed by (a , b+c),(b , c+a)a n d(c , a+b) ...

    Text Solution

    |

  15. If the points A(4,3)a n dB(x ,5) are on the circle with centre O(2,3),...

    Text Solution

    |

  16. Find the equation of the perpendicular bisector of AB, where A and B ...

    Text Solution

    |

  17. If the point (x , y) is equidistant from the points (a+b , b-a) and ...

    Text Solution

    |

  18. Find the distance between the points: (i) P(-6,7) andQ(-1,-5) (ii)R(a...

    Text Solution

    |

  19. Find the angle subtended at the origin by the line segment whose end ...

    Text Solution

    |

  20. Prove that the points (2,3),(-4,-6)a n d(1,3/2) do not form a triangle...

    Text Solution

    |