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

In an acute angled triangle ABC, AD is the median in it. Prove that : AD^(2) = (AB^(2))/2 + (AC^(2))/2 - (BC^(2))/4

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

In an isosceles triangle ABC, AB = AC and D is a point on BC produced. Prove that : AD^(2)=AC^(2)+BD.CD

The given figure shows an equilateral triangles ABC and D is point in AC. Prove that : (i) AD lt BD (ii) BC gt BD

In triangle ABC, AB=AC and BD is perpendicular to AC. Prove that : BD^(2)-CD^(2)=2CDxxAD

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)

The following figure shows a triangle ABC in which AD is a median and AE bot BC . Prove that 2AB^(2)+ 2AC^(2) = 4AD^(2) + BC^(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

The following figures shows a triangle ABC in which AD is median and AE bot BC. Prove that : 2AB ^(2) + 2AC^(2) = 4AD^(2)+ BC^(2)