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AP EAMCET201823 Apr 2018Evening ShiftMathematicsProperties of TrianglesActual

If I is the incentre of A B C and P₁, P₂, P₃ are respectively the radii of the circumcircles of the I B C, I C A and I A B , then P₁ P₂ P₃=

Options

  1. A2 R r
  2. B2 R r^2
  3. C2 R^2 r
  4. D4 R r

Correct answer

C. 2 R^2 r

Step-by-step solution

In I B C, B I C= 2 - A 2 , let circumcentre of I B C is C₁ , then B C₁ C= 2 + A 2 So, a / 2 P₁ = ( 2 + A 2 )= A 2 P₁= a 2 A 2 Similarly, P₂= b 2 B 2 and P₃= c 2 C 2 So, P₁ P₂ P₃= a b c 8 A 2 B 2 C 2 = a b c A 2 B 2 C 2 A B C =(2 R) (2 R^ )(2 R) r 4 R =2 R^2 r .

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