If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

If all the vertices of a triangle have integral coordinates, then the triangle may be (a) right-angle (b) equilateral (c) isosceles (d) none of these

If the coordinates of the vertices of a triangle are rational numbers, then which of the following points of the triangle will always have rational coordinates

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Find the point P in the interior of the triangle such that P B C is an equilateral triangle.

In triangle ABC if cotA +cot B +cot C=sqrt3 then prove that the triangle is an equilateral triangle

If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equilateral

If in any triangle ABC, cot A + cotB + cotC = sqrt(3) , prove that, the triangle is equilateral.

If the co-ordinate of three vertices of a- triangle are (9, 1, -3), (1.- 1, -5) and (3, 1, 3). Show that the triangle is equilateral

write the ratio of the angles of an equilateral triangle.

If for a triangle ABC , cot A+cotB+cotC= sqrt3 ,then show that the triangle is equilateral.