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AP EAMCET2004MathematicsProperties of Triangles

In a A B C , the correct formulae among the following are

Options

  1. Aonly I, II
  2. Bonly I,II
  3. Conly I,III
  4. DI,II,III

Correct answer

C. only I,III

Step-by-step solution

I. Since, 4 R A 2 B 2 C 2 aligned & = 4 a b c 4 (s-b)(s-c) b c (s-a)(s-c) a c & = a b c (s-a)(s-b) a b & = a b c 4 ^2 s a b c & = s =r aligned Hence, r=4 R A 2 B 2 C 2 II. Since, aligned & (s-a) A / 2=(s-a) (s-b)(s-c) s(s-a) & = s(s-a)(s-b)(s-c) s^2 & = s =r aligned Hence, r₁ (s-a) A 2 III. Since, s-c = s(s-a)(s-b) (s-c) =s (s-a)(s-b) s(s-c) =s c 2 =r₃ Hence r₃= s-c Therefore I and III statements are true but II is a false statement.

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