Statement−1: In a ΔABC, if a<b<c and r is in-radius and r1,r2,r3 are the exradii opposite to angle A,B,C respectively, then r<r1<r2<r3.
Statement−2 : For, ΔABC r1r2+r2r3+r3r1=r1r2r3r
A
Both statements are True and statement−2 is the correct explanantion of Statement−1
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B
Both statements are True but statement−2 is NOT the correct explanantion of Statement−1
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C
Statement−1 is True and statement−2 is False.
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D
Statement−1 is False and statement−2 is True.
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Solution
The correct option is B Both statements are True but statement−2 is NOT the correct explanantion of Statement−1 Statement−1 :
Given,a<b<c⇒Δs<Δs−a<Δs−b<Δs−c
We know, r=Δs,r1=Δs−a,r2=Δs−b,r3=Δs−c ⇒r<r1<r2<r3
Statement−2 :
Clearly, from the relations of inradius and exradii, we have:1r1+1r2+1r3=1r ⇒r1r2+r2r3+r3r1=r1r2r3r
Clearly, both statements are True but statement−2 is NOT the correct explanantion of Statement−1