Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In ABC , if A =90^ , then ( r ₂- r ₁ ) ( r ₃- r ₁ )=

Options

  1. Ar ₂ r ₃
  2. B2 r₂ r₃
  3. C4 r₂ r₃
  4. D2

Correct answer

B. 2 r₂ r₃

Step-by-step solution

In ABC A =90^ aligned & b^2+c^2=a^2 & 1 2 (b+c-a)^2=(b-a)(c-a) & (b-a)(c-a)=2(s-a)^2 & (b-a)(c-a) (s-a)^2 =2 aligned aligned & (1- s-b s-a ) (1- s-c s-a )=2 & (1- s-a s-b ) (1- s-a s-c )=2 & (r₂-r₁ ) (r₃-r₁ )=2 r₁ r₃ 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