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

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

In Fig , ABD is a triangle right angled at A and AC bot BD. show that AC^(2)=BC . DC

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

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

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