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Question Number 15894 by Tinkutara last updated on 15/Jun/17

If the angles of a triangle A B C be in

A . P ., then

(1) c^{2} = a^{2} + b^{2} - a b

(2) b^{2} = a^{2} + c^{2} - a c

(3) a^{2} = b^{2} + c^{2} - a c

(4) b^{2} = a^{2} + c^{2}

Commented by ajfour last updated on 15/Jun/17

(2) i s c o r r e c t, i f ∠ B = π / 3

2 c a \cos B = c^{2} + a^{2} - b^{2}

w i t h \cos B = π / 3

b^{2} = c^{2} + a^{2} - a c .

A n d o n e o f t h e a n g l e s n e e d b e π / 3 .

i f 2 B = A + C t h e n

2 B = π - B

B = π / 3 .

A n y o n e o f (1), (2), o r (3) c a n

b e c o r r e c t d e p e n d i n g o n w h i c h

a n g l e i s π / 3 .

Commented by Tinkutara last updated on 16/Jun/17

Thanks Sir!