Prove that the points (0,0) `(3, sqrt(3)) and (3, -sqrt(3))` are the vertices of an equilateral triangle.

Show that the points 1, (-1)/2 + i (sqrt3)/2 ,and (-1)/2 - i (sqrt(3))/(2) are the vertices of an equilateral triangle.

If the point (0,0),(2,2sqrt(3)), and (P ,q) are the vertices of an equilateral triangle, then (p ,q) is (a) (0,-4) (b) ( 4,4) c)(4,0) (d) (5,0)

Show that the complex numbers 3+3i , -3-3i(-3sqrt(3)+i3sqrt(3)) are the vertices of an equilateral triangle in the complex plane.

Prove that (sqrt(2),sqrt(2)) (-sqrt(2), -sqrt(2) ) and (-sqrt(6 ) , sqrt(6)) are ther vertices of an equilateral triangle.

If the three points (0, 1), (0, -1) and (x, 0) are vertices of an equilateral triangle, then the values of x are

Show that the points (a,a), (-a,-a) and (-asqrt(3),asqrt(3)) form an equilateral triangle .

Let P (sin theta, cos theta) (0 le theta le 2pi) be a point and let OAB be a triangle with vertices (0,0) , (sqrt(3/2),0) and (0,sqrt(3/2)) Find theta if P lies inside triangle OAB

If the vertices of a triangle are (sqrt(5,)0) , ( sqrt(3),sqrt(2)) , and (2,1) , then the orthocentre of the triangle is (sqrt(5),0) (b) (0,0) (c) (sqrt(5)+sqrt(3)+2,sqrt(2)+1) (d) none of these

Prove that the following are irrational. sqrt3 +sqrt5