# Angle sums of a triangle [closed]

Given only the external angles of a triangle circumscribed in an arc and given the angle at the arc's centre that is between the vertices of the triangle's base. solve the triangle if the base of this triangle is a chord to the circle of which the arc is a part.solve the inscribed triangle

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## closed as off-topic by Weapon of Choice, voldemort, Jack D'Aurizio, Ivo Terek, Morgan OAug 31 at 1:33

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Could you provide a link to this problem, if there's any? –  Américo Tavares Jun 24 '11 at 11:11
What does "solve the triangle" mean? Surely you can't find the sides - if you scale all the lengths by any non-zero number, the angles stay the same. –  Gerry Myerson Jun 24 '11 at 12:55
@Didier: Third bad sign: he hasn't answer any comments in nay of his questions –  leonbloy Jun 24 '11 at 13:58
@leonbloy: Indeed. –  Did Jun 29 '11 at 14:16

If you know the radius of the circular arc, then it's possible to find the length of the chord for which you know the subtended arc measure (if the radius is $r$ and the arc measure is $\alpha$, then the Law of Cosines applied to the triangle formed by the central angle and the chord says that the chord length $c$ satisfies $c^2=2r^2-2r^2\cos\alpha$). With one side length and all three interior angle measures, you can find a second side length by applying the Law of Sines, then use the Law of Cosines (or the Law of Sines) to find the third side length.