Question

In a triangle, if $r₁ > r₂ > r₃$ then

• A. $a>b>c$
• B. $a<b<c$
• C. $a>b$ and $b<c$
• D. $a<b$ and $b>c$

Hint:

In a triangle, if $r1 > r2 > r3$ then

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Ex-radii formulas: $r_1 = \frac{\Delta}{s-a}, r_2 = \frac{\Delta}{s-b}, r_3 = \frac{\Delta}{s-c}$.
Step 2: Evaluation
If $r_1>r_2>r_3$, then $\frac{1}{s-a}>\frac{1}{s-b}>\frac{1}{s-c}$.
Step 3: Final Calculation
Taking reciprocals: $s-a<s-b<s-c$.
Step 4: Conclusion
This implies $-a<-b<-c$, which means $a>b>c$.
Hence, the Answer is: (a)