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If the circle above has center Y and area 4Ï€...

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by elias.latour.apex » Wed Dec 27, 2017 4:51 am
Since both legs of the triangle start from the center and touch the edge of the circle, we know that they must be equal.
Therefore, the two angles formed by these legs must also be equal.
Since the given angle is 60º and since all angles of the triangle must add up to 180º, the sum of the unknown angles must be 120º.
Therefore, all angles of the triangle are 60º and it is an equilateral triangle.
Since the area of the circle is 4Ï€, the radius must be 2.

Therefore, all lengths of the triangle must be 2, and the perimeter must be 6.
Elias Latour
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