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

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`

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

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)

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

ABC is a triangle in which AB = AC and D is any point on BC. Prove that: AB^(2)- AD^(2) = BD. CD

ABC is an equilateral triangle where AB = a and P is any point in its plane such that PA = PB + PC. Then (PA^(2)+PB^(2)+PC^(2))/(a^(2)) is

Let I be the incentre of triangleABC . Using vectors prove that for any point P a(PA)^2+b(PB)^2+c(PC)^2=a(IA)^2+b(IB)^2+c(IC)^2+(a+b+c) (IP)^2 where a, b, c have usual meanings.

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let G be the centroid of the DeltaABC , whose sides are of lengths a,b,c. If P be a point in the plane of triangleABC , such that PA=1,PB=3, PC=4 and PG=2 , then the value of a^(2)+b^(2)+c^(2) is

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

RD SHARMA ENGLISH-COORDINATE GEOMETRY-All Questions
  1. If the point (x ,4) lies on a circle whose centre is at the origin an...

    Text Solution

    |

  2. If three points (x1,y1),(x2, y2),(x3, y3) lie on the same line, prove ...

    Text Solution

    |

  3. lf G be the centroid of a triangle ABC and P be any other point in the...

    Text Solution

    |

  4. (a) a^2+b^2 (b) a+b (c) a^2-b^2 (d) sqrt(a^2+b^2)

    Text Solution

    |

  5. Two vertices of a triangle are (3,-5)a n d(-7,4)dot If its centroid is...

    Text Solution

    |

  6. If A(5,2),B(2,-2)a n dC(-2, t) are the vertices of right angles triang...

    Text Solution

    |

  7. The length of a line segment is of 10 units and the coordinates of one...

    Text Solution

    |

  8. Find the coordinates of the circumcentre of the triangle whose vertice...

    Text Solution

    |

  9. Let the opposite angular points of a square be (3,4) and (1,-1) . Find...

    Text Solution

    |

  10. Show that A(6,4),B(5,-2) and C(7,-2) are the vertices of an isosceles...

    Text Solution

    |

  11. Points A(-1, y) and B(5,7) lie on a circle with centre O(2,-3y)dot Fin...

    Text Solution

    |

  12. Show that the points (1,-1),(5,2) and (9 ,5) are collinear.

    Text Solution

    |

  13. Show that four points (0,-1),(6,7),(-2,3)a n d(8,3) are the vertices o...

    Text Solution

    |

  14. If P and Q are two points whose coordinates are (a t^2,2a t)a n d(a/(t...

    Text Solution

    |

  15. If the two vertices of an equilateral triangle be (0,0),(3,sqrt(3)), f...

    Text Solution

    |

  16. The base A B of two equilateral triangles A B C and A B C ' with sid...

    Text Solution

    |

  17. On which axis do the following points lie? P(5,\ 0) (ii) Q(0,\ -2) ...

    Text Solution

    |

  18. Find the value of x , if the distance between the points (x ,\ -...

    Text Solution

    |

  19. Find the point on the xaxis which is equidistant from (2,\ 5)\ a n d \...

    Text Solution

    |

  20. Find a point on the y-axis which is equidistant from the point A(6,...

    Text Solution

    |