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...Matcourse notes on geometry circles and lines a circle is the set of points at xed distance r from given point its center called radius divides plane into two regions inside which less than o outside consists all having greater note that every line segment to has same length alinesegmentfromotoapointon isalsocalledaradius thisshouldcausenoconfusion aline connecting chord if passes through then it diameter as above we also use word denote number twice proposition k intersects in most proof suppose had three b c intersection with werst take up case this would have least side hence can both lie however by ruler axiom must oa ob since contradicts our assumption next not assume lies between draw segments oc oab oac obc are triangles fact they isosceles let be measure base angles triangle angle so add obtain each right impossible ab perpendicular bisector exercise prove preceding central while spent fair amount time determining when discussed explicitly calculating an except shall do now fir...