What Center Is Most Crucial?

Geometry Level 4

A triangle PQRPQR was drawn on a Cartesian plane such that there exists a point OO for which the distance PO=QO=RO\overline {PO } = \overline{QO} = \overline{RO} is equal to 4. And two of the vertices of this triangle have coordinates (1,3)(1,3) and (5,6)(5,6) .

Given that the sine of one of the interior angles of this triangle must always be a constant. Find this constant.

Give your answer to 3 decimal places.

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