Circles: Circle and Data C3

This is all I have so far:
Circles
IB Mathematics SL Type I

Luxjoria Thibodeaux
24 February 2013
Mr. Wallace
Period 6 In this task, I will analyze the positions of points in intersecting circles. The data is presented separately to distinguish between the original circle and the original circle’s relationship to circle 2 and circle 3. I will analyze each circle analytically and graphically to develop a general statement to represent the given data, as well as, consider any parameters, constraints, and suitable variables effecting my general statement.

Circle 1 - Original Data

r r P
P
O
O

Circle 1, the original data above, demonstrates a circle with a center point, O, a radius, r, and “any point” P.

Circles 2 - Original Data

C3
C3

A
A

P’ P’
P
P

C2
C2
O
O

C1
C1

Above are Circles c1 (orange), c2, (blue) and c3(black). Circle 1 is as listed in the original circle. Circle 2 has a center point of P, a radius of OP and AP, and a chord, OA. Point A is a point of intersection between c1 and c2. Circle 3 has a center point of A and a radius of r and AO. In addition, Point P’ is the intersection of C3 with line segment OP. As I analyzed the given line segments, I noticed that Circles, c1 and c3, share the same radius. As stated by the given data, r is equal to 1. Therefore, the radius of circle 1 and 3 are both 1.
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