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...Complex numbers in geometry yi sun mop how to use this handout we will identify the two dimensional real plane with one each point vector form associate corresponding number note throughout a lowercase letter denote that represents labeled by uppercase thisallowsustocomputegeometrictransformationseasily whichcanleadtosolutionsthatarequiteelegant problem tst let abc be triangle triangles pab and qac are constructed outside of such ap ab aq ac bap caq segments bq cp meet at r o circumcenter bcr prove ao pq when synthetic approaches have failed can computation cyclic quadrilateral abcd diagonals bd e lines ad bc f g h midpoints sides cd respectively ef is tangent circumcircle egh usamo p line passing through b c points where reections pa pb pc respect intersect collinear there general principles solve using approach reduce desired statement calculation done ways checking condition for parallel quadrilaterals collinearity or claim about angles distances given case you should just calculate...