In △ ABC, point O is a moving point on edge AC, and a straight line Mn parallel to BC is made through O. let Mn intersect the bisector of ∠ BCA at point e. the bisector of the outer angle of ∠ BCA intersects with point F 1. When point O moves on edge AC, will the quadrilateral BCFE be a diamond? If so, please prove. If not, explain the reason; 2. When point O moves to where, and △ ABC satisfies what conditions, the quadrilateral aecf is a square?

In △ ABC, point O is a moving point on edge AC, and a straight line Mn parallel to BC is made through O. let Mn intersect the bisector of ∠ BCA at point e. the bisector of the outer angle of ∠ BCA intersects with point F 1. When point O moves on edge AC, will the quadrilateral BCFE be a diamond? If so, please prove. If not, explain the reason; 2. When point O moves to where, and △ ABC satisfies what conditions, the quadrilateral aecf is a square?

∵ CE bisection ∠ ACB
∴∠ACE=∠BCE
∵MN‖BC
∴∠BCE=∠OEC
∴∠OEC=∠OCE
∴OE=OC
Similarly: of = OC
∴OE=OF
(2) When o is AC, the midpoint is a quadrilateral and aecf is a rectangle
It is proved that: OA = OC, OE = of
The quadrilateral aecf is a parallelogram
∵OE=OC=OF
∴∠ECF=90°
The quadrilateral aecf is a rectangle