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Unformatted text preview: scribed about these squares, with centers P and Q, intersect at M and also at another point N. Let N denote the point of intersection of the straight lines AF and BC. (a) Prove that the points N and N coincide. (b) Prove that the straight lines MN pass through a ﬁxed point S independent of the choice of M. (c) Find the locus of the midpoints of the segments PQ as M varies between A and B. 1959/6. Two planes, P and Q, intersect along the line p. The point A is given in the plane P, and the point C in the plane Q ; neither of these points lies on the straight line p. Construct an isosceles trapezoid ABCD (with AB parallel to CD ) in which a circle can be inscribed, and with vertices B and D lying in the planes P and Q respectively....
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 Spring '10
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 Quadratic equation, Euclidean geometry, Mathematics in medieval Islam

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