CirclesExercises jan 9 - PEM Level C 9 January 2010 Topics...

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PEM Level C 9 January 2010 Topics in Geometry - All about circles Exercises: 1. Prove that a line cannot cut a circle at more than two points. 2. Two circles intersect at two points. Prove that the length of the line segment passing through one point of intersection, parallel to the segment joining the centers, and terminating at the circles is double that of the segment joining the centers. 3. Suppose that the perpendicular bisectors of the three sides of a quadrilateral meet at a common point. Prove that the perpendicular bisector of the fourth side also passes through this common point. 4. One of the two points of intersection of two circles is A . (a) Show that a line segment through A joining points on the circles has the greatest length when the line segment is parallel to the line passing through the centers. (b) Suppose that the two circles have radii r and s , and that their points of intersection are at a distance t from each other. How long is the line segment that is greatest in (a)?
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