In the given figure ABC is a right triangle and right angled at B such that `/_BCA = 2/_BAC.`
Show that hypotenuse AC = 2BC.

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

ABC is a right angled triangle in which /_A = 90^@ and AB = AC . Show that /_B = /_C .

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).

In a right triangle ABC, right angled at B, if tan A=1, then verify that 2sinAcosA=1.

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) .

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

If Delta ABC is right triangle and if angleA = (pi)/(2) , then prove that cos^(2)B + cos^(2)C = 1

PQR is a triangle right angled at P and M is a point on QR such that PM bot QR . Show that PM^(2) = QM .MR.

In DeltaPQR is a right angled triangle, right angled at Q such that QR =-b and A(DeltaPQR)=a. If QNbotPR, then show that QN =(2a.b)/(sqrt(b^(2)+4a^(2))).