##
Chord Lines

----C-----
P----/ \-----
---/ \---
-/ \-
A/-------------Q--M-----------------\B

Let AB be a chord of a circle with center O and radius R. M is the
midpoint of AB and line OM intersects the circle at point C. Solve
each of the following in terms of R.
- Find AM and CM if AM equals 3*CM, 2*CM, CM, CM/2, or CM/3.
Can you solve the general case for AM=X*CM?
- Line segments are drawn from C to point Q on AM, from Q to point
P on the circle, and from P to A. Find CQ if CQ=QP=PA.
I believe there are multiple answers, so solve for CQ in terms
of CM (or AB). What is CQ if CM=R/2?

Source: Original. Based upon a design on the side of a building
in Rocklin, CA on I-80.

Solution

Mail to Ken