Find the points inside a `Delta` from which the sum of the squares of distance to the three sides is minimum.

A wire of length 36 cm is cut into two pieces . One of the pieces is to be made into a square and the other into a equilaterel triangle. Find the length of each piece so that the sum of the areas of the square and the triangle is minimum.

Find two numbers, each greater than or equal to - 2 whose sum is 1/2 so that the sum of square of the first and cube of the second is minimum.

Find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis.

Find three numbers in G.P. whose sum is 35 and sum of their squares is 525.

Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a cricle of radius = r units. If the sum of areas of the square and the circle so formed is minimum, then

Find the locus of a point whose sum of the distances from the origin and the line x = 2 is 4 units.

Find two positive numbers whose sum is 14 and their sum of squares is minimum .