If `A(x_1,y_1),B(x_2,y_2),` and `C(x_3,y_3)` are three non-collinear points such that `x1 2+y1 2=x2 2+y2 2=x3 2+y3 2,` then prove that `x_1sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin2C=0.`

If A(x_(1),y_(1)),B(x_(2),y_(2)), and C(x_(3),y_(3)) are three non-collinear points such that x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_(3)^(2)+y_(3)^(2), then prove that x_(1)sin2A+x_(2)sin2B+x_(3)sin2C=y_(1)sin2A+y_(2)sin2B+y_(3)sin2C=0

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 .

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 .

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 .

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

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(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 the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

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=3 a^4