Question

In a triangle ABC, if 8R²=a²+b²+c²d then the triangle is?​

Answer 1

Answer:

Mark as brainlist

Step-by-step explanation:

This essentially means sin2(A)+sin2(B)+sin2(C)=2. (This follows from sin rule.)

Replace C=π−(A+B) to get sin2(A+B)=cos2(A)+cos2(B).

Expand sin(A+B) and do the manipulations to get

2cos2(A)cos2(B)=2sin(A)sin(B)cos(A)cos(B)

which means cos(A)=0 or cos(B)=0 or cos(A)cos(B)=sin(A)sin(B)⇒cos(A+B)=0⇒cos(C)=0.

Hence either A=π/2 or B=π/2 or C=π/2.

So the triangle is a right-angled triangle.