Question

In any triangle ABC, a cot A + b cot B + c cot C =

• A. r + R
• B. r –R
• C. 2(r + R)
• D. 2(r –R)

Answer 1

Answer: (C)

2(r + R)

Answer 2

a cot A + b cot B + c cot C

then the triangle be equilateral then

a = b = c = x and A = B = C = 60°

∴ a cot A + b cot B + c cot C

= 3x cot 60°= $\sqrt { 3 }$x

by option (3) 2 (r + R)

= 2(r + 2r) = 6r

= = $\frac { 6 \frac { \sqrt { 3 } } { 4 } x ^ { 2 } } { \frac { 3 x } { 2 } }$= $\sqrt { 3 }$x