ABC is an isosceles triangle right angled at C. Prove that `AB^2` = `2AC^2`.

ABC is an isosceles triangle right angled at A. forces of magnitude 2sqrt(2),5 and 6 act along BC, CA and AB respectively. The magnitude of their resultant force is

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE^2+BD^2=AB^2+DE^2 .

BL and CM are medians of a triangle ABC right angled at A. Prove that 4 ( BL^2 + CM^2 ) = 5 BC^2 .

In fig., ABD is a triangle right angled at A and AC bot BD. Show that:- AB^2 =BC.BD .

ABC is an isosceles triangle with AC = BC. If AB^2 = 2AC^2 , prove that ABC is right triangle.

In Fig., ABD is a triangle right angled at A and AC bot BD . Show that: (i) AB^(2) = BC.BD (ii) AC^(2) = BC.DC (iii) AD^(2) = BD.CD

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2+AB^2= 2AD^2+1/2BC^2 . .

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AC ^(2) + AB ^(2) = 2 AD ^(2) + (1)/(2) BC ^(2).

ABC is an isosceles triangle with AB=AC and D is a point on an BC such that ADbotBC to prove that angleBAD=angleCAD ,