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JEE Main 2002
Exam
JEE Main
Year
2002
Subject
Mathematics
Chapter
Properties of Triangles

JEE Main 2002 · Mathematics · Properties of Triangles

In a triangle with sides a, b, c, r_1>r_2>r_3 (which are the...

In a triangle with sides a,b,c,r1>r2>r3a, b, c, r_1>r_2>r_3 (which are the ex-radii) then

Options

  1. Aa > b > c
  2. Ba < b < c
  3. Ca > b and b < c
  4. Da < b and b > c

Correct answer

A. a > b > c

Step-by-step solution

r1>r2>r3⇒Δs−a>Δs−b>Δs−c⇒s−a<s−b<s−c⇒−a<−b<−c⇒a>b>cr_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 \Rightarrow a>b>c
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