Circle Theorems in Motion

Also called

circle theorems · equal chords equal angles · angle subtended by a chord · angle at the centre · angle at the circumference · inscribed angle · angle in a semicircle · angles in the same segment · cyclic quadrilateral · opposite angles sum to 180 · chord · radius · diameter · arc of a circle · segment of a circle · वृत्त · जीवा · चक्रीय चतुर्भुज

Topics

• Equal chords of a circle subtend equal angles at the centre, and chords that subtend equal angles are equal.
• The angle an arc subtends at the centre is twice the angle it subtends at any point on the rest of the circle.
• The angle in a semicircle is a right angle: a diameter subtends 90° at every point on the circle.
• Angles in the same segment of a circle are equal: as P moves along its arc, the angle APB does not change.
• A cyclic quadrilateral has all four vertices on a circle; each pair of opposite angles adds up to 180°.
• If a line segment subtends equal angles at two points on the same side of it, the four points lie on one circle.
• The perpendicular from the centre of a circle to a chord bisects the chord.

About this model

A GLB file of about 289 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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