Prove that the centres of three equal circles touchinhg each other are the certices of an equilateral triangle.

Show that the angles of an equilateral triangle are 60^@ each.

A point moves so that the sum of the squares of the perpendiculars let fall from it on the sides of an equilateral triangle is constant. Prove that its locus is a circle.

The equation of the circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is-

Let's write the ratio of the three angles of equilateral triangle.

Each of the two equal circles passes through the centre of the other and the two circles intersect each other at the points. A and B.If a straight ine through the point A intersects the two circles at points C and D prove that Delta BCD is an equilateral triangle.

Prove that if the three medians of a triangle be equal , then it is an equilateral triangle.

Prove that the triangle of maximum area that can be incsribed in a given circle is an equilateral triangle.

Prove that the sum of the perpendiculars drawn from any interior point of an equilateral triangle to its sides then sum of three perpendiculars is equal to the altitude of the triangle.