`A A_1, B B_1a n dC C_1` are the medians of triangle `A B C` whose centroid is `Gdot` If points `A ,C_1, Ga n dB_1` are concyclic, then

AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that 2a^(2) = b^(2) + c^(2)

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

A(3,2)a n dB(-2,1) are two vertices of a triangle ABC whose centroid G has the coordinates (5/3,-1/3)dot Find the coordinates of the third vertex C of the triangle.

Let the area of a given triangle ABC be Delta . Points A_1, B_1, and C_1 , are the mid points of the sides BC,CA and AB respectively. Point A_2 is the mid point of CA_1 . Lines C_1A_1 and A A_2 meet the median BB_1 points E and D respectively. If Delta_1 be the area of the quadrilateral A_1A_2DE , using vectors or otherwise find the value of Delta_1/Delta

Find the equation of the medians of the triangle ABC whose vertices are A(2,5)B(-4,9)a n d\ C(-2,-1)dot

Find the lengths of the medians of a triangle whose vertices are A(-1,\ 3),\ \ B(1,\ -1) and C(5,\ 1) .

Straight lines y=m x+c_1 and y=m x+c_2 where m in R^+, meet the x-axis at A_1a n dA_2, respectively, and the y-axis at B_1a n dB_2, respectively. It is given that points A_1,A_2,B_1, and B_2 are concylic. Find the locus of the intersection of lines A_1B_2 and A_2B_1 .

Find the co-ordinates of the centroid of a triangle ABC whose vertices are : A(-1, 3), B(1, -1) and C(5, 1)

If A(-1,\ 3),\ \ B(1,\ -1) and C(5,\ 1) are the vertices of a triangle A B C , what is the length of the median through vertex A ?

If A(-1,\ 3),\ \ B(1,\ -1) and C(5,\ 1) are the vertices of a triangle A B C , what is the length of the median through vertex A ?