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

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

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

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

If Delta ABC is an isosceles triangle with angle C=90^(@) and AC=5 cm, then AB is

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that BC^(2) =CD^2 +3BD^(2) .

If Delta ABC is an isosceles triangle with hat(C ) = 90^(@) and AC = sqrt(8) cm then AB is :

In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE^(2)=3AC^(2)+5AD^(2).