Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2012MathematicsProperties of TrianglesActual

If in a triangle A B C, b+c 11 = c+a 12 = a+b 13 , then A is equal to

Options

  1. A5 / 7
  2. B1 / 5
  3. C35 / 19
  4. D19 / 35

Correct answer

B. 1 / 5

Step-by-step solution

Let b+c 11 = c+a 12 = a+b 13 =K in a triangle A B C . b+c=11 K, c+a=12 K, a+b=13 K On solving these, we get a=7 K, b=6 K, c=5 K Now we know, aligned & A= b^2+c^2-a^2 2 b c & = 36 K^2+25 K^2-49 K^2 2(6 K) 5 K = 1 5 aligned

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In a triangle ABC , BC =7, AC =8, AB = N and A = 2 3 . If 49 (3 C )+42= m n , where gcd ( m , n )=1 , then m + n is equal to________ 2024Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is π 2 and whose sides are in arithmetic progression. Suppose that 2023Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is π 2 and whose sides are in arithmetic progression. Suppose that 2023For a triangle A B C , the value of cos 2 A + cos 2 B + cos 2 C is least. If its inradius is 3 and incentre is M , then which of the following is NOT correct? 2023Let A B C be the triangle with A B = 1 , A C = 3 and ∠ B A C = π 2 . If a circle of radius r > 0 touches the sides A B , A C and also touches internally the circumci 2022Let a , b and c be the length of sides of a triangle A B C such that a + b 7 = b + c 8 = c + a 9 . If r and R are the radius of incircle and radius of circumcircle of the triangle 2022Consider a triangle P Q R having sides of lengths p , q and r opposite to the angles P , Q and R , respectively. Then which of the following statements is (are) TRUE? 2021In a triangle A B C , let A B = 23 , B C = 3 and C A = 4 . Then the value of cot A + cot C cot B is 2021 Full Properties of Triangles list All JEE Main PYQs