Cyclic quadrilaterals (= inscribed quadrilaterals) | plane geometry | elementary level

Episode 50.

Cyclic quadrilaterals (= inscribed quadrilaterals) | plane geometry | elementary level.

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

Definition. A quadrilateral is said to be cyclic (or inscribed) there exists a circle that passes through all 4 of its vertices.
Theorem. A quadrilateral is cyclic if and only if the sum of its opposite angles is equal to $180^{\circ}$.
Theorem. A quadrilateral is cyclic if and only if one of its angles is equal to the opposite external angle.
Theorem. A quadrilateral $ABCD$ is cyclic if and only if $\angle{ABD}=\angle{ACD}$.

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

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