The coordinates of the vertices `Ba n dC` of a triangle `A B C` are (2, 0) and (8, 0), respectively. Vertex `A` is moving in such a way that `4tan(B/2)tan(C/2)=1.` Then find the locus of `A`

If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) , respectively, then find angleABC .

The coordinates of the vertices A ,B and C of the triangle ABC are (-1,3),(1,-1) and (5,1) respectively . Find the length of the median through the vertex A.

B and C are the vertex of a triangle ABC with coordinate (2 , 0) and (8 , 0) respectively. Another vertex A moves in such a way that it satisfies the relation 4 " tan" (B)/(2) "tan" (C)/(2) = 1 . If the equation of locus of A is (x - 5)^(2)/5^2+ (y^(2))/(k^(2)) = 1 , then the value fo k is _

The coordinates of the vertices A, B and C of a triangle ABC are (0,5), (-1,-2) and (11,7) respectively . Find the coordinates of the foot of the perpendicular from B on AC.

The coordinate of the vertices B and C of the triangle ABC are (5,2,8) and (2, -3, 4) respectively, if the coordinates of the centroid of the triangle are (3, -1,3), then the coordinates of the vertex A are-

the coordinates of the vertices A,B,C of the triangle ABC are (7,-3) , (x,8) and (4,y) respectively , if the coordinates of the centroid of the triangle be (2,-1) , find x and y.

Is the coordinate of the three vertices of a recengle ABCD be A(1,0) , B (2,0) and D(-1,4), then the abscissa of C is -

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot

A B C is an equilateral triangle with A(0,0) and B(a ,0) , (a>0). L, M and N are the foot of the perpendiculars drawn from a point P to the side A B ,B C ,a n dC A , respectively. If P lies inside the triangle and satisfies the condition P L^2=P MdotP N , then find the locus of Pdot