If The Angles Of The Triangle ABC Are In A.P Then a2 + c2 - ac =______.

Angles are in A.P

Angle A = a – d

Angle B = a

Angle C = a + d

Angle A + Angle B + Angle C = 180°

= a – d + a + a + d = 180°

= 3a = 180°

= a = \( \frac{180}{3} \)

= a = 60°

Therefore, Angle B = 60°

As per cosine formula:

\(cos\; B = \frac{a^{2} + c^{2} – b^{2}}{2ac}\\\Rightarrow cos \; 60° = \frac{a^{2} + c^{2} – b^{2}}{2ac}\\\Rightarrow \frac{1}{2} = \frac{a^{2} + c^{2} – b^{2}}{2ac}\\\Rightarrow ac = a^{2} + c^{2} – b^{2}\\\Rightarrow a^{2} + c^{2} – ac = b^{2}\)


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