Question

In an equilateral triangle the ratio of sum of squares of altitudes to the sum of squares of sides

Answer 1

4AB2 + 4BC2 + 4AC 2 = AB2 + BC2 + AC2 + 4AD2 + 4BE2 + 4CF2 3(AB2 + BC2 + AC2) = 4(AD2 + BE2 + CF2)

Hence, three times the whole of squares of the sides of a triangle is equivalent to four times the entirety of squares of the medians of the triangle.