# The Special Point In A Triangle 1

Geometry Level 5

Let $$O$$ be a point in triangle $$ABC$$.

$$D$$ is the intersection of $$AO$$ and $$BC$$. $$E,F$$ are defined similarly.

$$X$$ is the intersection of $$EF$$ and $$AD$$. $$Y,Z$$ are defined similarly.

Let $$P$$ be the intersection of $$XY$$ and $$CF$$ and $$Q$$ be the intersection of $$XZ$$ and $$BE$$.

$$R$$ is the intersection of $$AP$$ with $$BC$$ and $$S$$ is the intersection of $$AQ$$ with $$BC$$.

Find: $$\dfrac{4 \times BS \times RC}{SC \times BR}$$.

The Special Point in A Triangle 2

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