Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201823 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In A B C if a=2, b= 6 and c= 3 +1 , then ^2 C- ^2 A=

Options

  1. A1+ 3 4
  2. B3 2
  3. C3 4
  4. D3 4

Correct answer

C. 3 4

Step-by-step solution

In A B C, a=2, b= 6 , c= 3 +1 We know that, aligned C & = a^2+b^2-c^2 2 a b = (2)^2+( 6 )^2-( 3 +1)^2 2 2 6 & = 4+6-3-1-2 3 4 6 & = 6-2 3 4 6 = 2 3 ( 3 -1) 4 6 C & = 3 -1 2 2 C & = 1- ( 3 2 2 )^2 [ = .1- ^2 ] & = 8-3-1+2 3 8 = 4+2 3 8 & = 2+ 3 4 = 1 2 + 3 4 aligned Now, aligned A & = b^2+c^2-a^2 2 b c = 6+3+1+2 3 -4 2 6 ( 3 +1) & = 6+2 3 2 6 ( 3 +1) = 3+ 3 6 ( 3 +1) = 3 ( 3 +1) 6 ( 3 +1) aligned aligned A & = 1 2 A & = 1- ( 1 2 )^2 = 1 2 aligned aligned & Now, ^2 C- ^2 A & = ( 1 2 + 3 4 )^2- ( 1 2 )^2= 1 2 + 3 4 -

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