An equilateral triangle ABC has one vertex at (2, 0) and orthocenter at `(1,1/sqrt3)`. Let `P=(1/2,1/4)` and distances of P from the side BC, CA, AB are respectively x, y and z then x+y+z is equal to

If (2,1,3), (3,2,5),(1,2,4) are the mid points of the sides BC,CA,AB, of Delta ABC respectively, then the vertex A is

One side of an equilateral triangle is the line 3x+4y+8=0 and its centroid is at P(1,1) . Find the length of a side.

One side of an equilateral triangle is 3x+4y=7 and its vertex is (1,2). Then the length of the side of the triangle is

One side of an equilateral triangle is 3x+4y=7 and its vertex is (1,2). Then the length of the side of the triangle is

A point 'P' is an arbitrary interior point of an equilateral triangle of side 4. If x, y, z are the distances of 'P' from sides of the triangle then the value of (x+y+z)^(2) is equal to -

A point 'P' is an arbitrary interior point of an equilateral triangle of side 4. If x, y, z are the distances of 'P' from sides of the triangle then the value of (x+y+z)^(2) is equal to -

A point P is an arbitrary interior point of an equilateral triangle of side 4. If x, y, z are the distances of 'P' from sides of the triangle then the value of (x+y+z)^(2) is equal to -

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).