Circle theorems - the opposite angles in a cyclic quadrilateral add up to 180°

Описание: Circle theorems - the opposite angles in a cyclic quadrilateral add up to 180°, with proof
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A cyclic quadrilateral is a four sided shape where all four vertices lie on the circumference of a circle. The opposite angles in a cyclic quadrilateral add up to 180°.

This video includes a proof of this theorem. It also illustrates that rectangles, squares, and right kites, are all cyclic quadrilaterals.

Suitable for UK GCSE, IB MYP, US grades 9+. Typically taught to students aged 14 and above.

Other videos:
Angle at the centre of a circle is twice the angle at the circumference:    • Circle theorems - angle at centre of circl...  
Angle in a semicircle is a right angle:    • Circle theorem - the angle in a semicircle...  

Related articles:
Opposite angles in a cyclic quadrilateral add up to 180°: https://graphicmaths.com/gcse/geometr...
Angle at the centre of a circle is twice the angle at the circumference: https://graphicmaths.com/gcse/geometr...
Angle in a semicircle is a right angle: https://graphicmaths.com/gcse/geometr...

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This video was created using generativepy, a free and open source Python library for creating mathematical art and animations, available from https://github.com/martinmcbride/gene...