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phrasing results in terms of secant lines instead of chords can help to unify statements. As an example of this consider the result:
:If two secant lines contain chords and in a circle and intersect at a point that is not on the circle, then the line segment lengths satisfy .If the point lies inside the circle this is Euclid III.35, but if the point is outside the circle the result is not contained in the Elements. However, Robert Simson following Christopher Clavius

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