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AP EAMCET201920 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

In a ( A B C ), with usual notation, match the items in List-I with the items in List-II and choose the correct option.

Options

  1. A( array lllll A & B & C & D 4 & 3 & 1 & 5 array )
  2. B( array lllll A & B & C & D 5 & 4 & 3 & 2 array )
  3. C( array lllll A & B & C & D 3 & 1 & 2 & 5 array )
  4. D( array lllll A & B & C & D 4 & 5 & 2 & 1 array )

Correct answer

C. ( array lllll A & B & C & D 3 & 1 & 2 & 5 array )

Step-by-step solution

( aligned & (A) r₁ r₂ 4 R-r₁-r₂ r₁+r₂ = [ ^2 (s-a)(s-b) . & . 4 R-4 R C 2 ( A 2 B 2 + B 2 A 2 ) 4 R C 2 ( A 2 B 2 + B 2 A 2 ) ] & = ^2 (s-a)(s-b) 4 R (1- ^2 C 2 ) 4 R ^2 C 2 aligned ) ( aligned & = ^2 (s-a)(s-b) C 2 & = ^2 (s-a)(s-b) (s-a)(s-b) s(s-c) = ^2 = & (B) r₂ (r₃+r₁ ) r₁ r₂+r₂ r₃+r₃ r₁ = s-b ( s-c + s-a ) (s-a)+(s-b)+(s-c) (s-a)(s-b)(s-c) & = (s-b) 3 s-a-b-c 2 s-a-c (s-a)(s-c) = (b) s(s-a)(s-b)(s-c) =b aligned ) ( aligned & (C) a c = (A-B) (B-C) A C = (A-B) (B-C) & A (B-C)= (A-B) C & A( B C- C B) & =( A B-

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