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AP EAMCET2013MathematicsProperties of Triangles

In any A B C, r₁ r₂+r₂ r₃+r₃ r₁ is equal to

Options

  1. A^2 r^2
  2. Br
  3. C2 r
  4. D^2

Correct answer

A. ^2 r^2

Step-by-step solution

aligned & In A B C, & = s-a s-b + s-b r₁ r₂+r₂ r₃+r₃ r₁ s-c + s-c s-a & = ^2 (s-a)(s-b)(s-c) [s-c+s-a+s-b] aligned aligned & = ^2 3 s-(a+b+c) (s-a)(s-b)(s-c) ( 2 s=a+b+c) & = ^2(3 s-2 s) (s-a)(s-b)(s-c) = ^2 s ( ^2 s ) & [ ^2 s =(s-a)(s-b)(s-c) ] & = s^2 ^2 ^2 = ^2 ( s )^2 = ^2 r^2 [ r= s ] aligned

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