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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)  4R2

(C) 8R2

(D)  16Rr2

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

(A)  3/2

(B)  3/4

(C)  3

(D)  6

1 Answer

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by (53.5k points)
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Best answer

Correct option  (B)(A)(D)

1.  See Fig.



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