ABC is a triangle, right angled at B, M is a point on BC. Prove that :
`AM^(2) + BC^(2) = AC^(2) + BM^(2)`

In Fig. 3, ABC is a right triangle, right angled at C and D is the mid-point of BC. Prove that AB^2 = 4AD^2 - 3AC^2 .

ABC is a triangle in which AB = AC and D is any point on BC. Prove that: AB^(2)- AD^(2) = BD. CD

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)

ABC is a isosceles right angled triangle, right angled at C. prove that AB^(2) = 2AC^(2)

In the given figure, triangle ABC is a right triangle with angleB=90^(@) and D is mid-point of side BC. Prove that : AC^(2)=AD^(2)+3CD^(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)

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

ABC is a triangle right angled at C. If AB=25cm and AC=7cm, find BC.

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