MathDB

Problem 3

Part of 2002 Mongolian Mathematical Olympiad

Problems(2)

prove that lines are concurrent with incircle intouch points

Source: Mongolian MO 2002 Grade 10 P3

4/9/2021
The incircle of a triangle ABCABC with AB≠BCAB\ne BC touches BCBC at A1A_1 and ACAC at B1B_1. The segments AA1AA_1 and BB1BB_1 meet the incircle at A2A_2 and B2B_2, respectively. Prove that the lines AB,A1B1,A2B2AB,A_1B_1,A_2B_2 are concurrent.
geometry
sets equal in terms of integral parameter

Source: Mongolian MO 2002 Teachers P3

4/9/2021
Find all positive integer nn for which there exist real number a1,a2,…,ana_1,a_2,\ldots,a_n such that {aj−ai∣1≤i<j≤n}={1,2,…,n(n−1)2}.\{a_j-a_i|1\le i<j\le n\}=\left\{1,2,\ldots,\frac{n(n-1)}2\right\}.
parameterization