AP EAMCET20224 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual
In a triangle A B C , r 1 cot A 2 + r 2 cot B 2 + r 3 cot C 2 =
Options
- As
- B2 s
- C3 s
- Ds 2
Correct answer
C. 3 s
Step-by-step solution
Recall that cot A 2 = s s - a ∆ and r 1 = ∆ s - a . i.e. r 1 cot A 2 + r 2 cot B 2 + r 3 cot C 2 = ∆ s - a × s s - a ∆ + ∆ s - b × s s - b ∆ + ∆ s - c × s s - c ∆ = 3 s