1. II1 + II2 + II3 is equal to

Question

Let I be the in-centre and I₁, I₂, I₃ be the ex-centre opposite to angle A, B, C, respectively, in ΔABC. If α , β,γ  be the circumradius of ∆BIC, ∆AIC and ∆AIB, respectively, and R, r, r₁, r₂, r₃ have their usual meaning, then

1.  II₁ + II₂ + II₃ is equal to

(A)  2R(sinA/2 + sinB/2 + sinC/2)

(B)  4R(sinA/2 + sinB/2 + sinC/2)

(C)  4R(cosA/2 +  cosB/2 + cosC/2)

(D)  4RsinA/2 + sinB/2 + sinC/2

2.  α , β,γ   is equal to

(A)  2R²r

(B)  4R²r 

(C) 8R²r 

(D)  16Rr²

3.  II₁/α  + II₂/β + II₃/γ is equal to

(A)  3/2

(B)  3/4

(C)  3

(D)  6

Answer 1

Correct option  (B)(A)(D)

1.  See Fig.

2.  

3.