If `(x_1, y_1), (x_2, y_2), (x_3, y_3)` are vertices of equilateral triangle such that `(x_1-2)^2+(y_1-3)^2=(x_2-2)^2+(y_2-3)^2=(x_3-2)^2+(y_3-3)^2` then

If (x_i,y_i),i=1,2,3 are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2 , then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3)

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

If (x_(i),y_(i)),i=1,2,3, are the vertices of an equilateral triangle such that (x_(1)+2)^(2)+(y_(1)-3)^(2)=(x_(2)+2)^(2)+(y_(2)-3)^(2)=(x_(3)+2)^(2)+(y_(3)-3)^(2) then find the value of (x_(1)+x_(2)+x_(3))/(y_(1)+y_(2)+y_(3))

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

If (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2) =(x_(3)-2)^(2)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sum y_(1)+3sum z_(1)

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of traingle ABC and x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2) , then show that x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0 .

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

If A(3x_(1),3y_(1)),B(3x_(2),3y_(2)),C(3x_(3),3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+x_(2)+x_(3),y_(1)+y_(2)+y_(3)) then the /_ABC=