In an equilateral triangle ABC, BE is perpendicular to side CA. Prove that:
` AB^(2) + BC^(2) +CA^(2) = 4BE^(2)`

In an equilateral triangleABC, AD is the altitude drawn from A on the side BC. Prove that 3AB^(2) = 4AD^(2)

In figure - 6 in an equilateral triangle ABC, AD_|_BC, BE_|_AC and CF_|_AB . Prove that 4(AD^(2)+BE^(2)+CF^(2))=9AB^(2)

In a right triangle ABC, right angled at A, AD is drawn perpendicular to BC. Prove that: AB^(2)-BD^(2)= AC^(2)-CD^(2)

In an equilateral triangle ABC, D is a point on side BC such that B D=1/3B C . Prove that 9A D^2=7A B^2 .

The given figure shows a triangle ABC, in which AB gt AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^(2) +AC^(2) =2BE^2 +2AE^2

In Figure -6 , in an equilateral triangle ABC, AD is perpendicular to BC , BE is perpendicular to AC and CF is perpendicular to AB . Prove that 4 (AD^2 +BE^2 +CF^2)=9AB^2

ABC is an equilateral triangle, P is a point in BC such that BP : PC =2 : 1. Prove that : 9 AP^(2) =7 AB^(2)

In triangle ABC, AB > AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^2 +AC^2=2AE^2 +2BE^2

The given figure shows a triangle ABC, in which AB gt AC . E is the mid-point of BC and AD is perpendicular to BC. Prove that AB^(2)- AC^(2)= 2BCxxED .

P and Q are the mid-points of the CA and CD respectively of a triangle ABC, right angled at C. Prove that: 4AQ^2 = 4AC^2 + BC^2 , 4BP^2 = 4BC^2 + AC^2 , and 4(AQ^2 + BP^2) = 5AB^2 .