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AP EAMCET202119 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

In ∆ A B C , suppose the radius of the circle opposite to angle A , B and C is denoted by r 1 , r 2 and r 3 . If r 1 = 2 , r 2 = 3 , r 3 = 6 and R is the radius of the circumcircle, then the value of r 1 + r 2 + r 3 - r =

Options

  1. A4 R
  2. B3 R
  3. C2 R
  4. DR

Correct answer

A. 4 R

Step-by-step solution

For △ A B C , exradii r 1 = △ s - a , r 2 = △ s - b , r 1 = △ s - c and inradius r = △ s , where s is the semi-perimeter of the triangle and r is the radius of in-circle. And, △ = s ( s - a ) ( s - b ) ( s - c ) = a b c 4 R Now, r 1 + r 2 + r 3 - r = △ s - a + △ s - b + △ s - c - △ s = △ × s s - b s - c + s s - a s - c + s s - a s - b - s - a s - b s - c s ( s - a ) ( s - b ) ( s - c ) = △ × s s - b s - c + s s - a s - c + s s - a s -

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