# What Center Is Most Crucial?

Geometry Level 4

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

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