Maths-
General
Easy

Question

If the angles of the Δ ABC are in A.P then 3R2=1

  1. bc
  2. b2c
  3. abc
  4. b2

hintHint:

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

The correct answer is: b2


    W e space k n o w space t h a t space fraction numerator a over denominator sin A end fraction equals fraction numerator b over denominator sin B end fraction equals fraction numerator c over denominator sin C end fraction equals 2 R space a n d
G i v e n space t h a t space a n g l e s space i n space A. P. space w h i c h space m e a n s comma
sin A space plus space sin C space equals 2 sin B
fraction numerator a over denominator 2 R end fraction space plus space fraction numerator c over denominator 2 R end fraction space equals space 2 cross times fraction numerator b over denominator 2 R end fraction space space space space space left curly bracket space G i v e n space R equals fraction numerator 1 over denominator square root of 3 end fraction space right curly bracket
fraction numerator a over denominator 2 R end fraction space plus space fraction numerator c over denominator 2 R end fraction space equals space b over R
a space plus space c space equals space 2 b

    s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

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