# Concyclic Points.

Suppose there exists a triangle $$\triangle{ABC}$$ where $$P$$ and $$Q$$ are points on segments $$\overline{AB}$$ and $$\overline{AC}$$ respectively, such that:

(1) $$\overline{AP} = \overline{AQ}$$.

Let $$S$$ and $$R$$ be distinct points on segment $$\overline{BC}$$ such that:

(2) $$S$$ lies between points $$B$$ and $$R$$

(3) $$\angle{BPS} = \angle{PRS}$$, and $$\angle{CQR} = \angle{QSR}$$.

Prove that points $$P,Q,R,S$$ are concyclic points.

Note by Thomas Kim
4 years ago

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