Homework Help: maths

Posted by jenny on Friday, October 12, 2012 at 1:19pm.

Let ABC be a triangle in the plane. Find circles C0;C1; : : : ;C6 such that Cj
has exactly j points in common with the boundary of ABC (this \boundary"
consists of the line segments AB, BC, CA). Is it possible to nd a circle C7
with 7 points in common with the boundary of ABC?
(Just use trial and error for this question - draw lots of circles and triangles
how do I do this?

maths - Steve, Friday, October 12, 2012 at 3:41pm
Of course not.

Each line can intersect any circle in at most two points.

The three lines can thus intersect a circle in at most 6 points.
maths - jenny, Friday, October 12, 2012 at 4:46pm
how do I draw them to prove it.

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