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In a triangle with sides a,b,c,r_{1}> r_{2}> r_{3}  ( which are the ex-­radii) then

Option: 1

a> b> c\; \;


Option: 2

\; a< b< c\; \;


Option: 3

\; a> b\, and\, b< c\; \;


Option: 4

\; a< b\, and\, b> c


Answers (1)

best_answer

As learnt ,

the ex-radii of a triangle are given by 

r_{1} = \frac{\Delta }{s-a} \\ \\ r_{2} = \frac{\Delta }{s-b} \\ \\ r_{3} = \frac{\Delta }{s-c} \\

where, r1, r2, r3 are the ex-radii of triangle for the ex-circles in front of vertices A,B and C respectively.

Now, as r_{1}> r_{2}> r_{3} \\ \\ \Rightarrow \frac{\Delta }{s-a}> \frac{\Delta }{s-b} > \frac{\Delta }{s-c}\\ \\ \Rightarrow s-a< s-b< s-c

                                 \Rightarrow a> b> c

Posted by

Ritika Kankaria

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