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...Geometry revisited before transformations adam kelly april this document is a rather brief summary of the rst three chapters h s m coxeter and l greitzer in no ways eshed out most cases just contains important results diagrams contents points lines connected with triangle interest circumcenter centroid orthocenter angle bisectors incenter incircles excircles steiner lehmus theorem orthic medial euler line nine point circle some properties circles power radical axis simson ptolemy collinearity concurrence quadrilaterals varignon cyclic brahmagupta formula napoleon triangles menelaus pappus perspective desargues pascal extended law sines for abc circumradius r b c sina sinb sinc ceva cevians ax by cz one through each vertex are concurrent if only bx cy za xc ya zb denition centre circumscribed about circumcircle o intersection perpendicular sides typically radius denoted that join vertices to midpoints opposite called medians intersect at g dissected its into six smaller equal area divid...