The correct option is B False
r=4RsinA2sinB2sinC2Now consider,cos(A)+cos(B)+cos(C)=2cos((A+B)2)cos((A−B)2)−(2cos2((A+B)2)−1)=2(cos((A−B)2))−cos((A+B)2)cos((A+B)2)+1=4sin(A2)sin(B2)sin(C2)+1
It is useful to remember the identity, cos(A) + cos(B) + cos(C) ≤32 though the proof is a little beyond the scope of this chapter
Therefore, 4sin(A2)sin(B2)sin(C2)+1≤32SinA2SinB2SinC2≤12.12.12=18⇒r<4R(18)=R2
∴ Given statement is false