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OpenStudy (anonymous):
Suppose that the segement P Q is a diameter of the circle C = C(X, XP ) and Z ∈ C \ {P, Q}. Show that in Euclidean Geometry ∠P ZQ is a right angle. Draw a diagram to illustrate your argument. Does your proof rely on Euclid’s Parallel Postulate? Is the conclusion true in hyperbolic gemetry?
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