Angle in a circle for School Maths Lab

Quick Answer: Angle in a circle for School Maths Lab is a geometry teaching aid for the circle theorems about angles subtended by an arc. Students use it to compare the angle at the centre with the angle at the circumference, and to check that angles in the same segment are equal.

The Circle Theorems This Aid Demonstrates

The central result is that an arc subtends at the centre of a circle an angle twice the angle it subtends at any point on the remaining part of the circle. Students fix an arc, measure the angle it makes at the centre and then the angle at a point on the circumference, and find the first is double the second. Moving the point around while keeping the arc fixed shows two more facts: the angle at the circumference does not change, so angles in the same segment are equal, and when the arc is a semicircle the angle becomes 90 degrees.

Doing this physically matters because the theorem is easy to state but hard to believe from one textbook diagram. Several measurements with different arcs and different points give students their own evidence before they study the formal proof, which uses the isosceles triangles formed by radii. The aid can then be used in reverse, for exercises in which one angle is given and the other must be found.

Construction of angle-in-a-circle aids varies: some use a board with pins and elastic cords, others a printed disc with movable arms or cut-out sectors. Confirm the form of this item before ordering, and keep protractors ready for measuring.

Applications

• Verifying that the angle at the centre is twice the angle at the circumference on the same arc
• Showing that angles in the same segment of a circle are equal
• Demonstrating that the angle in a semicircle is a right angle
• Setting up find-the-angle exercises before the formal proof

Care & Handling

• Return any movable parts to a neutral position before storage so hinges or cords are not left under strain.
• Keep the aid flat and dry; a warped board or disc distorts the angles students measure.
• Clean pencil marks with a soft eraser or damp cloth rather than abrasive cleaners that remove printed scales.

Specifications

Why Choose LabEquip

Secondary maths teachers and lab coordinators buy this aid for the circle geometry unit, often with a Circular Geoboard on which students explore the same theorems with elastic bands. Both are listed in LabEquip’s Mathematics School Lab Products; enquire through the contact page.

Frequently Asked Questions

What does ‘angle subtended by an arc’ mean?

It is the angle formed at a point by two lines drawn from that point to the two ends of the arc. The same arc subtends one angle at the centre and a different angle at a point on the circumference, and the aid lets students compare the two.

Why is the angle at the centre twice the angle at the circumference?

Join the point on the circumference to the centre and extend the line. It splits the figure into two isosceles triangles whose equal sides are radii. In each triangle the exterior angle at the centre equals twice a base angle, and adding the two parts gives the result.

Why is the angle in a semicircle 90 degrees?

The ends of a semicircle’s arc lie on a diameter, so the arc subtends a straight angle of 180 degrees at the centre. By the centre-angle theorem, the angle at the circumference is half of that, which gives a right angle.

How accurate will students’ measurements be?

With a school protractor, readings usually agree with the theorem to within a degree or two. Small differences are a useful talking point about measurement error, and they show why a proof is needed to establish the result for every case.

How is this different from a circular geoboard?

This aid is set up for the angle theorems. A circular geoboard is a general board of pins arranged in a circle on which students stretch elastic bands to make chords, polygons and angles, so it covers the same theorems plus inscribed polygons and fractions of a turn.

How are angles in the same segment demonstrated?

Keep the arc fixed and move the point around the major arc on the circumference. Each angle measured there comes out the same, which is the theorem that angles in the same segment of a circle are equal.

Last Updated: September 2026