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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