If cot (A/2)=(b+c)/a.show that `/_\ABC` is right angled.

If sin^2A + sin^2B= sin^2 C ,show that /_\ABC is right-angled.

The length of the sides of a triangle are a+b , ab-1 and sqrt((a^2+1)(b^2+1)) . Show that it is a right angled triangle.

In ∆ABC , AD _|_ BC such that AD^2 = BD.CD . Prove that ∆ABC is right angled at A.

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

In an isosceles triangle ABC if AC=BC and AB^2 = 2AC^2 , prove that /_C is a right angle.

In the triangle ABC,AB=p^2-q^2,BC=p^2+q^2 and CA=2pq then prove that triangleABC is right angled.Which of the angles of the triangle is right angle?

The length of the sides of a triangle are ax-by , ay+bx and sqrt((a^2+b^2)(x^2+y^2)) . Show that it is a right angled triangle.

In the triangle ABC, BC+CA=m^2+2mn-n^2 , CA+AB=(m+n)^2 and AB+BC=2m^2 . Show that it is a right angled triangle.

In /_\PQR , the line segment PS is perpendicular to QR and PS^2=QS×RS . Show that the triangle is a right angled one.

In the triangle ABC, BC = m^2 -n^2 , AC =3 mn and AB = m^2+n^2 . Prove that it is a right angled triangle.