This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1995 Bulgaria National Olympiad, 4
Tags: inradii , midpoint , equal circles , equilateral , geometry
Points $A_1,B_1,C_1$ are selected on the sides $BC$,$CA$,$AB$ respectively of an equilateral triangle $ABC$ in such a way that the inradii of the triangles $C_1AB_1$, $A_1BC_1$, $B_1CA_1$ and $A_1B_1C_1$ are equal. Prove that $A_1,B_1,C_1$ are the midpoints of the corresponding sides.

Ukrainian TYM Qualifying - geometry, 2015.20
Tags: inradii , geometry , geometric inequality , ratio
What is the smallest value of the ratio of the lengths of the largest side of the triangle to the radius of its inscribed circle?