If the angles of a triangle ABC be in A.P., then (1) c^2 = a^2 + b^2 − ab (2) b^2 = a^2 + c^2 − ac (3) a^2 = b^2 + c^2 − ac (4) b^2 = a^2 + c^2


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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

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