Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20225 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC s [ r₁-r a + r₂-r b + r₃-r c ]=

Options

  1. A1 r₁ + 1 r₂ + 1 r₃
  2. Br₁+r₂+r₃
  3. Cr₁ r₂ r₃
  4. D1 r - 1 r₁ + 1 r₂ + 1 r₃

Correct answer

B. r₁+r₂+r₃

Step-by-step solution

r=( s - a ) A / 2=( s - b ) B / 2=( s - c ) C / 2 aligned & r₁= s A / 2, r₂= s B / 2, r₃= s C / 2 & r₁-r= s A / 2-( s - a ) A / 2= a A / 2 & r₁-r a = A 2 aligned Similarly, r₂-r b = B 2 , r₃-r c = C 2 aligned & s [ A 2 + B 2 + C 2 ] & =s A 2 +s B 2 +s C 2 & =r₁+r₂+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