A theorem about two circles intersecting on the sides of a triangle | plane geometry | intermediate

Episode 59.

A theorem about two circles intersecting on the sides of a triangle | plane geometry | intermediate.
A theorem about two circles intersecting on the sides of a triangle | plane geometry | intermediate level.

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

Theorem. Let $ABC$ be a triangle. Let $\omega_1$ be a circle passing through the vertices $A$ and $C$ and intersecting the sides $AB$ and $BC$ at the points $P$ and $Q$ respectively. Let $\omega_2$ be the circumcircle of the triangle $BQP$, and let $O$ be its center. Then $BO \perp AC$.

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

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