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Found problems: 1

2022 German National Olympiad, 5
Tags: geometry , geometry proposed , tangent , tangent lines , touching circles
Let $ABC$ be an equilateral triangle with circumcircle $k$. A circle $q$ touches $k$ from outside in a point $D$, where the point $D$ on $k$ is chosen so that $D$ and $C$ lie on different sides of the line $AB$. We now draw tangent lines from $A,B$ and $C$ to the circle $q$ and denote the lengths of the respective tangent line segments by $a,b$ and $c$. Prove that $a+b=c$.