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I've been struggling at this problem for about 3 days now. I've posted it on a couple forums will no answers, so maybe I'll get a solution here. Thanks in advance!

Plain Diagram: http://www.swivelgames.com/projects/ideas/circlepoints/getseglength_simpler.png

Known: A, B, C, P, R, T, Z, h, w

Need: D, E, F; Length of dcef and ef segments

Y axis is inverted!!

(0,0) is at top left corner of rectangle

Known Data

h = 600

w = 800

C is at (w/2,h2) = (400,300)

R is at (400,0)

P is at (400,600)

A is at (534,88)

B is at (740,296)

T is at (534,0)

Z is at (534,600)

∠TAB = 135°

∠ZAB = 45°

∠RCE = ∠TAB

∠PCE = ∠ZAB

Problem Solving

∠ZFE = 90 - ∠PCE

∠ZFE = 45°

segCP = segRC = 400

segCF = sin(∠PCF) × segCP

segCF = sin(45) × 400

segCF = 282.8427125

The Question!

Now all I really need is the length of segEF to solve the problem, since we know that segDE = segAB.

So segDF = segDE + segEF

Can anyone help me get segEF?

Something to note:This is a real-world problem where ∠TAB will be anywhere from 0° to 360°, which in-turn would affect what side and position F would be. And ∠RCFalways= ∠TAB

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