AP EAMCET2004MathematicsProperties of Triangles

In a A B C,(a-b)^2 ^2 C 2 +(a+b)^2 ^2 C 2 is equal to

Options

Aa^2
Bc^2
Cb^2
Da^2+b^2

Correct answer

B. c^2

Step-by-step solution

We have, aligned & (a-b)^2 ^2 C 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 & =a^2(1)+b^2(1)-2 a b ( ^2 C 2 - ^2 C 2 ) & =a^2+b^2-2 a b C & [ array c C= a^2+b^2-c^2 2 a b or a^2+b^2-2 a b C=c^2 array ] & =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 )= 2025 If 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 = 2025 In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025 In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025 In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025 In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025 In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025 In 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