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

Tags were heavily modified to better represent problems.

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Found problems: 2

2016 Sharygin Geometry Olympiad, 7
Tags: construction , geometry , geometric transformation , symmedian point , circumcenter , circumcircle , reflection
Restore a triangle by one of its vertices, the circumcenter and the Lemoine's point. [i](The Lemoine's point is the intersection point of the reflections of the medians in the correspondent angle bisectors)[/i]

2021 Saudi Arabia Training Tests, 23
Tags: parallelogram , geometry , symmedian point , circumcircle , inradius
Let $ABC$ be triangle with the symmedian point $L$ and circumradius $R$. Construct parallelograms $ ADLE$, $BHLK$, $CILJ$ such that $D,H \in AB$, $K, I \in BC$, $J,E \in CA$ Suppose that $DE$, $HK$, $IJ$ pairwise intersect at $X, Y,Z$. Prove that inradius of $XYZ$ is $\frac{R}{2}$ .