Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202613 April 2026Morning ShiftMathematicsProperties of TrianglesActual

With usual notations, in ABC , (b - c)^2 ^2 A 2 + (b + c)^2 ^2 A 2 =

Options

  1. Aa^2
  2. Bb^2 - c^2
  3. Ca^2 + b^2 + c^2
  4. D0

Correct answer

A. a^2

Step-by-step solution

Expanding the given expression: (b^2 + c^2 - 2bc) ^2 A 2 + (b^2 + c^2 + 2bc) ^2 A 2 Grouping the terms with (b^2 + c^2) and 2bc : (b^2 + c^2)( ^2 A 2 + ^2 A 2 ) - 2bc( ^2 A 2 - ^2 A 2 ) Using the trigonometric identities ^2 + ^2 = 1 and ^2 - ^2 = 2 : b^2 + c^2 - 2bc A By the cosine rule in ABC , a^2 = b^2 + c^2 - 2bc A . Thus, the given expression is equal to a^2 . Answer: a^2

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 MHT CET PYQs