A four-sided figure with all its corners on a circle. Why its opposite angles add to 180 degrees, how to tell whether a quadrilateral is cyclic, and problems that use these facts.
3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson
Created by StemPy LabA cyclic quadrilateral has all four corners on one circle. The sum of each pair of opposite angles is . We prove this with the angle at the centre, find unknown angles, and decide which four-sided figures can be cyclic.
An outside corner of a cyclic quadrilateral equals the inside angle opposite to it. We prove this theorem, prove the converse of the main theorem by contradiction, and use both to show that four points lie on one circle.
We put the theorem, its converse and the exterior angle together. We show that a trapezium is cyclic exactly when its legs are equal, learn how to chase angles through a figure, and test coordinates and sets of angles by program.
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