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Statement-1: In any !ABC, if a : b : c =...

Statement-1: In any `!ABC`, if a : b : c = 4 : 5 : 6, then R:r=16:17.
Statement-2: In any `!ABC,R/r=(abc)/(4s)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement- 2 is True.

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the given statements regarding triangle \(ABC\) where the sides are in the ratio \(a : b : c = 4 : 5 : 6\). We will also use the relationships between the circumradius \(R\) and the inradius \(r\). ### Step-by-Step Solution: 1. **Assign Variables to the Sides**: Let the sides of triangle \(ABC\) be: \[ a = 4x, \quad b = 5x, \quad c = 6x ...
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