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.

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant.Prove that its locus is an ellipse.

The locus of a point which moves such that the sum of the squares of the distances from the three vertices of a triangle is constant, is a circle whose centre is at the:

Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9, the locus of such point is

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9, the locus of such point

The sum of the perpendiculars drawn from an interior point of an equilateral triangle is 20 cm. What is the length of side of the triangle ?

Prove that the sum of the squares of the reciprocals of two perpendicular diameter of an ellipse is constant.

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.