Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201824 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In A B C , (a-b)^2 ^2 ( A+B 2 )+(a+b)^2 ^2 ( C 2 )=

Options

  1. Ab^2
  2. Ba^2
  3. Cc^2
  4. Da^2+b^2-c^2

Correct answer

C. c^2

Step-by-step solution

aligned & In A B C, A+B+C= & A+B= -C & =(a-b)^2 ^2 ( A+B 2 )+(a+b)^2 ^2 C 2 & = [a^2+b^2-2 a b ] ^2 ( -C 2 ) & + [a^2+b^2+2 a b ] ^2 C 2 aligned aligned & = (a^2+b^2 ) ^2 C 2 -2 a b ^2 C 2 & + (a^2+b^2 ) ^2 C 2 +2 a b ^2 C 2 & =a^2+b^2-2 a b ( ^2 C 2 - ^2 C 2 ) & =a^2+b^2-2 a b C & =a^2+b^2-2 a b ( a^2+b^2-c^2 2 a b ) & a^2+b^2-a^2-b^2+c^2=c^2 aligned

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All AP EAMCET PYQs