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

2012 Oral Moscow Geometry Olympiad, 3
Given an equilateral triangle $ABC$ and a straight line $\ell$, passing through its center. Intersection points of this line with sides $AB$ and $BC$ are reflected wrt to the midpoints of these sides respectively. Prove that the line passing through the resulting points, touches the inscribed circle triangle $ABC$.
midpoint isotomic tangent geometry incircle

2021 Sharygin Geometry Olympiad, 10
Prove that two isotomic lines of a triangle cannot meet inside its medial triangle. [i](Two lines are isotomic lines of triangle $ABC$ if their common points with $BC, CA, AB$ are symmetric with respect to the midpoints of the corresponding sides.)[/i]
isotomic geometry