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A geometry (combinatorics) problem that is not orz

Source: 2023 China TST Problem 5

March 15, 2023
geometrycombinatoricsChina TST

Problem Statement

Let △ABC\triangle ABC be a triangle, and let P1,⋯ ,PnP_1,\cdots,P_n be points inside where no three given points are collinear. Prove that we can partition △ABC\triangle ABC into 2n+12n+1 triangles such that their vertices are among A,B,C,P1,⋯ ,PnA,B,C,P_1,\cdots,P_n, and at least n+n+1n+\sqrt{n}+1 of them contain at least one of A,B,CA,B,C.
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