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Answer:
equilateral triangle: all angles 60°
Step-by-step explanation:
It can be shown easily that an equilateral triangle meets the requirement. It is a little more difficult to show that the requirement forces an equilateral triangle.
In an equilateral triangle, the incenter and the circumcenter are the same point: the centroid. The centroid is half as far from the side as it is from the vertex, so the requirement ri/rc = 1/2 is demonstrated by that property.
