The tangential quadrilateral formed by centers of 4 tangent circles | plane geometry | intermediate

Episode 74.

The tangential quadrilateral formed by centers of 4 tangent circles | plane geometry | intermediate.
The tangential quadrilateral formed by the centers of a circular chain of 4 tangent circles | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Theorem. Let $\omega_1$, $\omega_2$, $\omega_3$, $\omega_4$ be circles with centers $O_1$, $O_2$, $O_3$, $O_4$ respectively such that $\omega_1$ touches $\omega_2$, $\omega_2$ touches $\omega_3$, $\omega_3$ touches $\omega_4$, and $\omega_4$ touches $\omega_1$. Then the quadrilateral $O_1O_2O_3O_4$ is tangential.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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