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Question: In a \(\triangle A B C\) \(r _ { 1 } < r _ { 2 } < r _ { 3 }\), then...

In a △ABC\triangle A B C r1<r2<r3r _ { 1 } < r _ { 2 } < r _ { 3 }, then

A

a<b<ca < b < c

B

a>b>ca > b > c

C

b<a<cb < a < c

D

a<c<ba < c < b

Answer

a<b<ca < b < c

Explanation

Solution

In a △ABC\triangle A B C r1<r2<r3r _ { 1 } < r _ { 2 } < r _ { 3 }

1r1>1r2>1r3\frac { 1 } { r _ { 1 } } > \frac { 1 } { r _ { 2 } } > \frac { 1 } { r _ { 3 } }⇒ s−aΔ>s−bΔ>s−cΔ\frac { s - a } { \Delta } > \frac { s - b } { \Delta } > \frac { s - c } { \Delta }

⇒ (s−a)>(s−b)>(s−c)( s - a ) > ( s - b ) > ( s - c )

⇒ −a>−b>−c- a > - b > - c ⇒ a<b<ca < b < c.