Vector probe!

Geometry Level pending

Let the scalene triangle A B C ABC . On the in-bisector line of the angle B A C BAC let the arbitrary point P P . Denote E , F E,F respectively as the orthocenter of the triangle A B P ABP and A C P ACP . Let S S be the midpoint of the arc B A C BAC . Then which of the following is always true

B E → + C F → = S B → − S C → \overrightarrow{BE}+\overrightarrow{CF} = \overrightarrow{SB}-\overrightarrow{SC} B E → + C F → = S A → + P E → + P F → \overrightarrow{BE}+\overrightarrow{CF} = \overrightarrow{SA}+ \overrightarrow{PE}+ \overrightarrow{PF} B E → + C F → = S A → + E F → \overrightarrow{BE}+\overrightarrow{CF} = \overrightarrow{SA}+\overrightarrow{EF} B E → + C F → = 2 S A → \overrightarrow{BE}+\overrightarrow{CF} = 2\overrightarrow{SA}

Danish Ahmed by Danish Ahmed , 24, India

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