Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202312 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In ABC , m B = 3 and m C = 4 . Let point D divide BC internally in the ratio 1: 3 , then ( B A D) ( C A D) has the value

Options

  1. A1 3
  2. B1 3
  3. C1 6
  4. D2 3

Correct answer

C. 1 6

Step-by-step solution

In ABD , aligned & ( BAD ) BD = ( ABD ) AD & ( BAD ) x = 3 2 AD & AD = 3 x 2 ( BAD ) aligned In ADC , aligned & ( CAD ) DC = ( ACD ) AD & ( CAD ) 3 x = 1 2 AD & AD = 3 x 2 ( CAD ) aligned From (i) and (ii), we get aligned & 3 x 2 ( BAD ) = 3 x 2 ( CAD ) & ( BAD ) ( CAD ) = 6 6 = 1 6 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 MHT CET PYQs