# Find sufficient conditions in which the triangle $ABC$ is located inside the domain traced by the triangle $DEF$.

Let us consider two triangles $$ABC$$ and $$DEF$$ in the plane.

My question is: Find sufficient conditions in which the triangle $$ABC$$ is located inside the domain traced by the triangle $$DEF$$.

Let $$X$$ be a point in the plane of $$\Delta DEF$$.

Thus, if $$\measuredangle DXE+\measuredangle EXF+\measuredangle DXF=360^{\circ}$$ then $$X$$ is placed inside the $$\Delta DEF$$.

If it's not so then $$X$$ is not placed inside the triangle.

You can check it for any vertex of $$\Delta ABC$$.

Another way.

If for all point $$Y$$ of the plane the ray $$XY$$ intersects some side of the $$\Delta DEF$$ then $$X$$ is placed inside the $$\Delta DEF$$.

If there is ray $$XY$$, which does not intersect sides of $$\Delta DEF$$ then $$X$$ is not placed inside the $$\Delta DEF$$.