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...Red mop lecture june po shen loh common abbreviations for geometry problems given triangle abc a b and c are the lengths of sides opposing vertices respectively s is semiperimeter r inradius circumradius facts part i extended law sines sina revisited page let p q be radii two circles through touching bc at then pq ceva d e ca f ab suppose that af bdce fbdcea prove ad cf concurrent trig sincadsinabesinbcf sindabsinebc sinfca centroid lies way down each median steiner lehmus such angle bisectors equal isosceles srr ra rb rc three excircles orthic feet altitudes determine called orthocenter incenter euler line o g h circumcenter collinear hg go...