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AP EAMCET201822 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In a A B C, D, E and F respectively are the points of contact of the incircle with the sides A B, B C and C A such that A D= , B E= and C F= , then + + =

Options

  1. AR^2
  2. B2 R
  3. C2 r
  4. Dr^2

Correct answer

D. r^2

Step-by-step solution

From figure array ll ar ( A B C)= ar ( A O B)+ ar ( B O C)+ ar ( C O A) & .S= 1 2 c r+ 1 2 a r+ 1 2 b r [where ar ( A B C)=S ] & S= 1 2 r(a+b+c) & S= 1 2 r(2 s) [where s is semi perimeter] & S=r s r= S s r^2= s^2 s^2 & r^2= s(s-a)(s-b)(s-c) s^2 & r^2= + + [ 2 s=2 +2 +2 ] array

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