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Triangle with circumscribed circle

The triangle in the circle

Choose a triangle by rearranging A,B and C - Find the radius of the circle. - Divide the length of one side of the triangle by the sine of the angle opposite that side - Rearrange your triangle and calculate again. What do you notice? Is this the same for the other sides and respective angles? Can you come up with a rule? (A generalization?) extra: Does it work for different types of triangles? (What types of triangle do you know?) Can you find an arrangement for which it doesn't work? Explain to what extend it doesn't work