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
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.
midpoint inradii equal circles geometry equilateral

Ukrainian TYM Qualifying - geometry, 2015.20
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?
ratio geometric inequality inradii geometry geometric inequalities