Ring of Theorem for School Maths Lab

Quick Answer: Ring of Theorem is a circular teaching model for the angle theorems of the circle, such as the angle at the centre being double the angle at the circumference and the angle in a semicircle being a right angle. Students use the Ring of Theorem to compare angles formed at different points on the circle and see which ones stay fixed.

Circle Angle Theorems on One Model

Circle theorems describe angles that stay the same while the points forming them move. The angle an arc makes at the centre equals twice the angle it makes at any point on the rest of the circle. Any two angles standing on the same arc, with their vertices in the same segment, are equal. For a semicircle, the arc stands on a diameter, so the angle at the centre measures 180° and the angle at the circumference 90°.

A drawing shows one position at a time, which leaves students unsure whether a result is general. A model on which the vertex can be set at several points around the ring lets the class watch the angle at the circumference hold steady as the vertex moves along one arc, and switch to its supplement when the vertex crosses into the other segment. That observation leads directly to the theorem that opposite angles of a cyclic quadrilateral add up to 180°.

Models sold under this name are generally described as covering the angle in a semicircle, angles in the same segment and the centre-angle property. Confirm the full list, and how points are set on the ring, before ordering.

Applications

• Comparing the angle at the centre with the angle at the circumference on the same arc, which it doubles
• Demonstrating that angles in the same segment are equal
• Confirming that the angle in a semicircle measures 90°
• Leading into the cyclic quadrilateral theorem and its converse

Specifications

Care & Handling

• Keep any pointers, pins or strings that come with the ring in a labelled bag fixed to the model.
• Wipe the surface with a dry cloth and do not write over printed angle markings.
• Store the model flat so that the ring keeps its shape.

Why Choose LabEquip

Schools that already use the Angle in a circle and Angle Property of Cyclic Quadrilateral models often add this ring as one aid that brings the main angle results together. All three are in LabEquip’s Mathematics School Lab Products range, and the contact page can confirm exactly what the ring shows.

Frequently Asked Questions

What is the angle at the centre theorem?

An arc makes an angle at the centre of a circle that is double the angle it makes at any point on the rest of the circle. If the angle at the centre measures 100 degrees, every angle at the circumference standing on the same arc measures 50 degrees.

Why is the angle in a semicircle a right angle?

A diameter makes an angle of 180 degrees at the centre, because it is a straight line. By the angle at the centre theorem, the angle it subtends at any point on the circle is half of that, which is 90 degrees.

What does angles in the same segment mean?

A chord divides a circle into two segments. Angles formed by joining the ends of the chord to any points in the same segment are all equal. Points in the other segment give angles that are supplementary to them.

How is the cyclic quadrilateral theorem connected?

The opposite vertices of a cyclic quadrilateral lie in opposite segments of the same chord. Their angles at the centre together make a full turn of 360 degrees, so the angles at the circumference add up to half of that, 180 degrees.

Why use a model instead of drawing circles?

A drawing shows one position, so students may think a result is a coincidence of that particular figure. A model lets the class try many positions quickly and see the angle stay the same, which makes the need for a general proof clearer.

Which classes study circle theorems?

Circle angle theorems are part of secondary geometry, typically in the early secondary years, and they are revised for competitive examinations. The model also gives older students a quick reminder of the results.

Last Updated: September 2026