In this diagram,[br][br]Line p is the perpendicular bisector of DC. [br][br]Point C is a point on circle with center A.[br]Point E is the intersection of p and radius AC.

[b][color=#c51414]Directions:[/color][/b][br][br]Fill in the blanks below: [br][br]Since the radius of any circle never changes, it is said to be _______________________. [br][br]This implies radius AC is _______________________. [br][br]This also means means (AE + EC) is _______________________. [br][br]Since E lies on p (the perpendicular bisector of DC , we know ___ = ____. [i]Why is this?[/i][br][br][color=#c51414]Since (AE + EC) is ____________________, and since EC = ____________________, it also must be true that the quantity[br]AE + _____ is CONSTANT, regardless of where point E lies. [br][br]This implies that point E is guaranteed to lie on a/an ___________________ with points A and D serving as its _____________![/color]