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Cybermusings
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First of all, remember that minor arcs always equal twice their inscribed angle.
So minor arc OP=70 deg
And since OR and PQ are parallel, we know that angle QPR = angle PRO, so minor arc QR =70
Now, we know that OR is the diameter of the circle, so arc of that line is 180 deg (half a circle).
Thus, arcs QR+OP+PQ have to = 180, which leads to 140+PQ=180
PQ=40, but we need this in terms of pi, divide it by 360 deg. = 1/9 of the circumference of the circle.
C=pi*d and d=18 from the problem statement, so PQ=1/9*18*pi=2*pi
I've had a problem like this before that I got stuck on because I didn't remember that minor arc = 2* inscribed angle, that's the key!
Hope that helps.
