Question:
In a triangle, if $r₁ > r₂ > r₃$ then
In a triangle, if $r₁ > r₂ > r₃$ then
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In a triangle, if $r1 > r2 > r3$ then
Updated On: Apr 15, 2026
- $a>b>c$
- $a<b<c$
- $a>b$ and $b<c$
- $a<b$ and $b>c$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Ex-radii formulas: $r_1 = \frac{\Delta}{s-a}, r_2 = \frac{\Delta}{s-b}, r_3 = \frac{\Delta}{s-c}$.
Step 2: Analysis
If $r_1>r_2>r_3$, then $\frac{1}{s-a}>\frac{1}{s-b}>\frac{1}{s-c}$.
Step 3: Evaluation
Taking reciprocals: $s-a<s-b<s-c$.
Step 4: Conclusion
This implies $-a<-b<-c$, which means $a>b>c$.
Final Answer: (a)
Ex-radii formulas: $r_1 = \frac{\Delta}{s-a}, r_2 = \frac{\Delta}{s-b}, r_3 = \frac{\Delta}{s-c}$.
Step 2: Analysis
If $r_1>r_2>r_3$, then $\frac{1}{s-a}>\frac{1}{s-b}>\frac{1}{s-c}$.
Step 3: Evaluation
Taking reciprocals: $s-a<s-b<s-c$.
Step 4: Conclusion
This implies $-a<-b<-c$, which means $a>b>c$.
Final Answer: (a)
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