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AP EAMCET202318 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , r ₁+ r ₂+ r ₃- r =

Options

  1. A4 R
  2. B2 R
  3. C4 R A
  4. D4 R A

Correct answer

A. 4 R

Step-by-step solution

r₁+r₂+r₃-r aligned & =4 R [ A 2 B 2 C 2 + A 2 B 2 C 2 . & .+ A 2 B 2 C 2 - A 2 B 2 C 2 ] & =4 R [ C 2 [ A 2 B 2 + A 2 B 2 ] . & .+ C 2 ( A 2 B 2 - A 2 B 2 ) ] & 4 R [ C 2 ( A+B 2 )+ C 2 ( A+B 2 ) ] & =4 R [ C 2 ( 2 - C 2 )+ C 2 ( 2 - C 2 ) ] & =4 R [ C 2 C 2 + C 2 C 2 ]=4 R . aligned

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