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KVPY2011MathematicsProperties of Triangles

In triangle A B C , we are given that 3 A+4 B=6 and 4 B+3 A=1 . Then the measure of the angle C is -

Options

  1. A30^
  2. B150^
  3. C60^
  4. D75^

Correct answer

A. 30^

Step-by-step solution

Square & add both equations array r 9+16+24 ( A + B )=37 ( A + B )= 1 2 A + B = 6 C= 5 6 (wrong) A+B= 5 6 C= 6 because C = 5 6 array does not follow equation 3 A+4 B=6

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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 KVPY PYQs