In this diagram,[br][br][color=#888]Line p[/color] is the perpendicular bisector of CD. [br][br]Point C is a point on circle with center A.[br][color=#c51414]Point H_1[/color] is the intersection of p and ray 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 (AH_1 – CH_1) is _________________. [br][br]Since H_1 lies on p (the perpendicular bisector of DC) , we know ____ = ______. Why is this?[br][br][color=#c51414]Since (AH_1 – CH_1) is ______________, and since CH_1 = ______, it also must be true that the quantity[br]AH_1 – _____ is CONSTANT as well, regardless of where point H_1 lies. [br][br]This implies that point H_1 is guaranteed to lie on one branch of a/an _______________________with points A and D serving as its __________![/color]