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That’s odd, these problems are so hard! Where are they even from?

Geo????? → Geo?????? → Geo???? → Geo?????

In what follows, triangle *P**Q**R* is an **acute** triangle, and point *S* is in the interior of triangle *P**Q**R*.

- Given that
*Q*= (171.316,−92.366),*R*= (6.258,−264.479),*S*= (48.501,−139.162), and that*S*is the centroid of*P**Q**R*, find*P*. - Given that
*P*= (−243.537,179.039),*Q*= (338.676,341.390),*R*= (−30.976,−36.228), and that*S*is the incenter of*P**Q**R*, find*S*. - Given that
*P*= (27.908,−102.106),*Q*= (439.054,296.796),*R*= (−73.114,203.114), and that*S*is the orthocenter of*P**Q**R*, find*S*. - Given that
*P*= (−243.537,179.039),*R*= (−30.976,−36.228),*S*= (−56.792,67.804), and that*S*is the incenter of*P**Q**R*, find*Q*. - Given that
*P*= (27.908,−102.106),*Q*= (439.054,296.796),*S*= (18.153,−91.237), and that*S*is the orthocenter of*P**Q**R*, find*R*. - Given that
*P*= (79.667,101.833),*Q*= (−20.136,−72.144),*R*= (−17.585,114.724), and that*S*is the symmedian point of*P**Q**R*, find*S*. - Given that
*P*= (79.667,101.833),*R*= (−17.585,114.724),*S*= (33.942,89.051), and that*S*is the symmedian point of*P**Q**R*, find*Q*. - Given that
*Q*= (439.054,296.796),*R*= (−73.114,203.114),*S*= (3.950,122.419), and that*S*is the orthocenter of*P**Q**R*, find*P*. - Given that
*P*= (−243.537,179.039),*Q*= (338.676,341.390),*S*= (20.520,106.335), and that*S*is the incenter of*P**Q**R*, find*R*. - Given that
*Q*= (−20.136,−72.144),*R*= (−17.585,114.724),*S*= (9.098,−61.302), and that*S*is the symmedian point of*P**Q**R*, find*P*. - Given that
*P*= (15.056,−80.644),*R*= (6.258,−264.479),*S*= (22.241,−142.971), and that*S*is the centroid of*P**Q**R*, find*Q*. - Given that
*Q*= (338.676,341.390),*R*= (−30.976,−36.228),*S*= (35.932,−30.136), and that*S*is the incenter of*P**Q**R*, find*P*. - Given that
*P*= (79.667,101.833),*Q*= (−20.136,−72.144),*S*= (19.049,−70.431), and that*S*is the symmedian point of*P**Q**R*, find*R*. - Given that
*P*= (27.908,−102.106),*R*= (−73.114,203.114),*S*= (34.156,−99.532), and that*S*is the orthocenter of*P**Q**R*, find*Q*. - Given that
*P*= (15.056,−80.644),*Q*= (171.316,−92.366),*R*= (6.258,−264.479), and that*S*is the centroid of*P**Q**R*, find*S*. - Given that
*P*= (15.056,−80.644),*Q*= (171.316,−92.366),*S*= (84.647,−46.540), and that*S*is the centroid of*P**Q**R*, find*R*.

m_{3} − m_{10} | m_{8} + m_{12} | m_{2} | m_{16} | Km_{15} − m_{11} | Im_{12} − m_{11} | Hm_{9} − m_{2} | Gm_{13} + m_{16} |

m_{6} − m_{7} | m_{4} − m_{11} | m_{5} + m_{7} | m_{3} − m_{15} | ||||

m_{1} − m_{12} | m_{12} | ||||||

m_{14} − m_{2} |