Polar graph: stuck on sketching a cardioid, something about chords

Sketch the cardioid with polar equation r=2(1+cos theta)

**Prove that for all the chords POQ of the cardioid which pass through the pole O, the length of PQ is constant.**

How do I do the green part?

I have gone as far as to deduce that if P (r1, theta1) and Q is (r2, theta2)

Then theta2=theta1-180

r2=2+2cos (theta1-180)

There isn't given a formula in the book to find the distance between two polar coordinates, I found one on net:

http://www.thestudentroom.co.uk/atta...1&d=1224276450

Here is the sketch of the graph:

http://www.thestudentroom.co.uk/atta...1&d=1224276450

I am stuck here for over two hours. Emergency help...I am drow...(Oops I gulped up some water)