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AP EAMCET2008MathematicsProperties of Triangles

Observe the following statements (I) In A B C, b ^2 C 2 +c ^2 B 2 =s (II) In A B C, A 2 = b+c 2 B=90^ Which of the following is correct?

Options

  1. ABoth I and II are true.
  2. BI is true, II is false.
  3. CI is false, II is true.
  4. DBoth I and II are false.

Correct answer

B. I is true, II is false.

Step-by-step solution

(I) Now, aligned & , b ^2 C 2 +c ^2 B 2 & =b s(s-c) a b +c s(s-b) a c & = s a (s-c+s-b) & = s a (2 s-(b+c))= s a a & =s aligned Statement Ist is true. array rlrl (II) Let A 2 & = b+c a & A 2 A 2 & = B+ C A & A 2 A 2 & = 2 ( B+C 2 ) ( B-C 2 ) 2 A 2 A 2 & A 2 & = ( B-C 2 ) & A 2 & = B-C 2 & A+C & =B array But A+B+C= , therefore B= 2 But given statement is A 2 = b+c 2 B=90^ . Statement-II is not true. Hence, option (2) is correct.

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