Through any given set of four distinct points P, Q, R and 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 points are called concyclic points.

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

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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?

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?

T P

and

T Q

are tangents from

T

to the circle with centre

O .

Then is it possible to draw a circle through the points

P, O, Q

and

T ?

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