We would like to construct a triangle $\triangle ABC$, if we know positions of three points from the set \{vertices, feet of the medians, feet of the altitudes, feet of the internal angle bisectors, circumcenter, incenter, orthocenter, centroid\}. Then we have $139$ problems, all non-trivial and significantly distinct. For example, the triple of points $\{A, B, C\}$ is trivial, the selection of the triple of points to be two vertices and the centroid of a triangle could be listed as $\{A, B, G\}, \{B, C, G\}$ or $\{A, C, G\}$, which are all analogous. Only $74$ of these problems are solvable and we present their constructions.
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