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Question

Statement1: 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.

Statement2 : For, ΔABC
r1r2+r2r3+r3r1=r1r2r3r

A
Both statements are True and statement2 is the correct explanantion of Statement1
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B
Both statements are True but statement2 is NOT the correct explanantion of Statement1
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C
Statement1 is True and statement2 is False.
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D
Statement1 is False and statement2 is True.
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Solution

The correct option is B Both statements are True but statement2 is NOT the correct explanantion of Statement1
Statement1 :
Given,a<b<cΔs<Δsa<Δsb<Δsc
We know, r=Δs,r1=Δsa,r2=Δsb,r3=Δsc
r<r1<r2<r3
Statement2 :
Clearly, from the relations of inradius and exradii, we have:1r1+1r2+1r3=1r
r1r2+r2r3+r3r1=r1r2r3r
Clearly, both statements are True but statement2 is NOT the correct explanantion of Statement1

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