Through any given set of four distinct points P, Q, R, S it is possible to draw at most ___circle(s).

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Solution

At most one circle can be drawn through a given set of four distinct points. These four points will then be referred to as 'concyclic points' (Lying on the same circle). It is also possible that no circle passes through all the four points.

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Q. Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

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Question 3
Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

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